@incollection{Biskup2009,
  author = {Biskup, Marek},
  title = {Reflection Positivity and Phase Transitions in Lattice Spin Models},
  editor = {Koteck{\'y}, Roman},
  booktitle = {Methods of Contemporary Mathematical Statistical Physics},
  series = {Lecture Notes in Mathematics},
  volume = {1970},
  pages = {1--86},
  publisher = {Springer},
  address = {Berlin, Heidelberg},
  year = {2009},
  doi = {10.1007/978-3-540-92796-9_1},
  eprint = {math-ph/0610025v2},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1007/978-3-540-92796-9_1},
  note = {arXiv version 2, 27 April 2009. Theorem 5.8, (5.34)--(5.35), printed p. 44; proof pp. 45--46},
}

@article{YangMills1954,
  author = {Yang, C. N. and Mills, R. L.},
  title = {{Conservation of Isotopic Spin and Isotopic Gauge Invariance}},
  journal = {Physical Review},
  volume = {96},
  number = {1},
  pages = {191--195},
  year = {1954},
  doi = {10.1103/PhysRev.96.191},
  url = {https://doi.org/10.1103/PhysRev.96.191},
}

@article{Wilson1974,
  author = {Wilson, Kenneth G.},
  title = {{Confinement of Quarks}},
  journal = {Physical Review D},
  volume = {10},
  number = {8},
  pages = {2445--2459},
  year = {1974},
  doi = {10.1103/PhysRevD.10.2445},
  url = {https://doi.org/10.1103/PhysRevD.10.2445},
}

@article{FILS1978,
  author = {Fr{\"o}hlich, J{\"u}rg and Israel, Robert and Lieb, Elliott H. and Simon, Barry},
  title = {{Phase Transitions and Reflection Positivity. {I}. General Theory and Long Range Lattice Models}},
  journal = {Communications in Mathematical Physics},
  volume = {62},
  number = {1},
  pages = {1--34},
  year = {1978},
  doi = {10.1007/BF01940327},
  url = {https://doi.org/10.1007/BF01940327},
}

@article{OsterwalderSeiler1978,
  author = {Osterwalder, Konrad and Seiler, Erhard},
  title = {{Gauge Field Theories on a Lattice}},
  journal = {Annals of Physics},
  volume = {110},
  number = {2},
  pages = {440--471},
  year = {1978},
  doi = {10.1016/0003-4916(78)90039-8},
  url = {https://doi.org/10.1016/0003-4916(78)90039-8},
}

@article{Gross1983Abelian,
  author = {Gross, Leonard},
  title = {{Convergence of {$U(1)_3$} Lattice Gauge Theory to Its Continuum Limit}},
  journal = {Communications in Mathematical Physics},
  volume = {92},
  number = {2},
  pages = {137--162},
  year = {1983},
  doi = {10.1007/BF01210842},
  url = {https://doi.org/10.1007/BF01210842},
}

@article{MagnenRivasseauSeneor1993,
  author = {Magnen, Jacques and Rivasseau, Vincent and S{\'e}n{\'e}or, Roland},
  title = {{Construction of {YM}$_4$ with an Infrared Cutoff}},
  journal = {Communications in Mathematical Physics},
  volume = {155},
  number = {2},
  pages = {325--383},
  year = {1993},
  doi = {10.1007/BF02097397},
  url = {https://doi.org/10.1007/BF02097397},
}

@article{Chatterjee2016,
  author = {Chatterjee, Sourav},
  title = {{The Leading Term of the {Yang--Mills} Free Energy}},
  journal = {Journal of Functional Analysis},
  volume = {271},
  number = {10},
  pages = {2944--3005},
  year = {2016},
  doi = {10.1016/j.jfa.2016.04.032},
  eprint = {1602.01222v6},
  archivePrefix = {arXiv},
  primaryClass = {math-ph},
  url = {https://arxiv.org/abs/1602.01222v6},
}

@incollection{Chatterjee2019Survey,
  author = {Chatterjee, Sourav},
  title = {{{Yang--Mills} for Probabilists}},
  editor = {Friz, Peter and K{\"o}nig, Wolfgang and Mukherjee, Chiranjib and Olla, Stefano},
  booktitle = {{Probability and Analysis in Interacting Physical Systems}},
  series = {Springer Proceedings in Mathematics \& Statistics},
  volume = {283},
  pages = {1--16},
  publisher = {Springer},
  year = {2019},
  doi = {10.1007/978-3-030-15338-0_1},
  eprint = {1803.01950},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1803.01950},
}

@misc{FariaVeigaOCarroll2019,
  author = {da Veiga, Paulo A. Faria and O'Carroll, Michael},
  title = {{On Thermodynamic and Ultraviolet Stability of {Yang--Mills}}},
  year = {2019},
  doi = {10.48550/arXiv.1903.09829},
  eprint = {1903.09829v2},
  archivePrefix = {arXiv},
  primaryClass = {math-ph},
  url = {https://arxiv.org/abs/1903.09829v2},
  note = {Preprint, version 2, 7 October 2019. No journal publication verified as of 16 October 2026.},
}

@article{FariaVeigaOCarroll2025,
  author = {da Veiga, Paulo A. Faria and O'Carroll, Michael},
  title = {{On {Yang--Mills} Stability Bounds and Plaquette Field Generating Function}},
  journal = {Reports on Mathematical Physics},
  volume = {95},
  number = {3},
  pages = {303--380},
  year = {2025},
  doi = {10.1016/S0034-4877(25)00035-7},
  eprint = {2205.07376v2},
  archivePrefix = {arXiv},
  primaryClass = {math-ph},
  url = {https://arxiv.org/abs/2205.07376v2},
}

@article{Brennecke2026,
  author = {Brennecke, Christian},
  title = {{On the Leading Order Term of the Lattice {Yang--Mills} Free Energy}},
  journal = {Journal of Statistical Physics},
  volume = {193},
  number = {7},
  pages = {83},
  year = {2026},
  doi = {10.1007/s10955-026-03649-4},
  eprint = {2511.07297},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://doi.org/10.1007/s10955-026-03649-4},
}

@article{FILS1980,
  author = {Fr{\"o}hlich, J{\"u}rg and Israel, Robert B. and Lieb, Elliott H. and Simon, Barry},
  title = {{Phase Transitions and Reflection Positivity. {II}. Lattice Systems with Short-Range and Coulomb Interactions}},
  journal = {Journal of Statistical Physics},
  volume = {22},
  number = {3},
  pages = {297--347},
  year = {1980},
  doi = {10.1007/BF01014646},
  url = {https://doi.org/10.1007/BF01014646},
}

@article{Balaban1984I,
  author = {Ba{\l}aban, Tadeusz},
  title = {Propagators and Renormalization Transformations for Lattice Gauge Theories. {I}},
  journal = {Communications in Mathematical Physics},
  volume = {95},
  number = {1},
  pages = {17--40},
  year = {1984},
  doi = {10.1007/BF01215753},
  url = {https://doi.org/10.1007/BF01215753},
  note = {Proposition 1.1, p. 33; formulas (1.11), (1.18), (1.39)--(1.44), (1.60)--(1.69), (1.103)},
}

@article{Balaban1984II,
  author = {Ba{\l}aban, Tadeusz},
  title = {Propagators and Renormalization Transformations for Lattice Gauge Theories. {II}},
  journal = {Communications in Mathematical Physics},
  volume = {96},
  number = {2},
  pages = {223--250},
  year = {1984},
  doi = {10.1007/BF01240221},
  url = {https://doi.org/10.1007/BF01240221},
  note = {Proposition 2.7 and Corollary 2.8, p. 249},
}

@article{Balaban1985Background,
  author = {Ba{\l}aban, Tadeusz},
  title = {Propagators for Lattice Gauge Theories in a Background Field},
  journal = {Communications in Mathematical Physics},
  volume = {99},
  number = {3},
  pages = {389--434},
  year = {1985},
  doi = {10.1007/BF01240355},
  url = {https://doi.org/10.1007/BF01240355},
  note = {Theorems 3.1--3.3, pp. 397--399; H{\"o}lder norms (3.40), p. 397, and nonendpoint first-gradient H{\"o}lder bounds (3.43), p. 398; extension (3.133), p. 422, and Theorem 3.12, p. 423; constrained covariance (3.148), (3.153), pp. 425--426; Theorem 3.13, p. 426. Only the stated identity-background portions are used},
}

@article{Dimock2013v2,
  author = {Dimock, Jonathan},
  title = {The Renormalization Group According to {Balaban}---{I}. Small Fields},
  journal = {Reviews in Mathematical Physics},
  volume = {25},
  number = {7},
  pages = {1330010},
  year = {2013},
  doi = {10.1142/S0129055X13300100},
  eprint = {1108.1335v2},
  archivePrefix = {arXiv},
  primaryClass = {math-ph},
  url = {https://arxiv.org/abs/1108.1335v2},
  note = {All numbered and printed-page locators refer to arXiv:1108.1335v2, 21 December 2012, not journal pagination: Appendix B, Theorem 27, p. 39, and connected hard-core graph estimate (323), p. 42. Only the finite graph bound is imported},
}

@article{Balaban1985Averaging,
  author = {Ba{\l}aban, Tadeusz},
  title = {{Averaging operations for lattice gauge theories}},
  journal = {Communications in Mathematical Physics},
  volume = {98},
  number = {1},
  pages = {17--51},
  year = {1985},
  doi = {10.1007/BF01211042},
  url = {https://doi.org/10.1007/BF01211042},
  note = {The reference-transport logarithmic averaging construction is equation (15), p. 19.},
}

@article{Balaban1985Regular,
  author = {Ba{\l}aban, Tadeusz},
  title = {{Spaces of regular gauge field configurations on a lattice and gauge fixing conditions}},
  journal = {Communications in Mathematical Physics},
  volume = {99},
  number = {1},
  pages = {75--102},
  year = {1985},
  doi = {10.1007/BF01466594},
  url = {https://doi.org/10.1007/BF01466594},
}

@article{Balaban1985UV,
  author = {Ba{\l}aban, Tadeusz},
  title = {{Ultraviolet stability of three-dimensional lattice pure gauge field theories}},
  journal = {Communications in Mathematical Physics},
  volume = {102},
  number = {2},
  pages = {255--275},
  year = {1985},
  doi = {10.1007/BF01229380},
  url = {https://doi.org/10.1007/BF01229380},
}

@article{Balaban1985Variational,
  author = {Ba{\l}aban, Tadeusz},
  title = {{The variational problem and background fields in renormalization group method for lattice gauge theories}},
  journal = {Communications in Mathematical Physics},
  volume = {102},
  number = {2},
  pages = {277--309},
  year = {1985},
  doi = {10.1007/BF01229381},
  url = {https://doi.org/10.1007/BF01229381},
}

@article{KoteckyPreiss1986,
  author = {Koteck{\'y}, Roman and Preiss, David},
  title = {{Cluster expansion for abstract polymer models}},
  journal = {Communications in Mathematical Physics},
  volume = {103},
  number = {3},
  pages = {491--498},
  year = {1986},
  doi = {10.1007/BF01211762},
  url = {https://doi.org/10.1007/BF01211762},
}

@article{Balaban1988RGII,
  author = {Ba{\l}aban, Tadeusz},
  title = {{Renormalization group approach to lattice gauge field theories. II. Cluster expansions}},
  journal = {Communications in Mathematical Physics},
  volume = {116},
  number = {1},
  pages = {1--22},
  year = {1988},
  doi = {10.1007/BF01239022},
  url = {https://doi.org/10.1007/BF01239022},
}

@article{Balaban1988Convergent,
  author = {Ba{\l}aban, Tadeusz},
  title = {{Convergent renormalization expansions for lattice gauge theories}},
  journal = {Communications in Mathematical Physics},
  volume = {119},
  number = {2},
  pages = {243--285},
  year = {1988},
  doi = {10.1007/BF01217741},
  url = {https://doi.org/10.1007/BF01217741},
}

@article{Balaban1983Green,
  author = {Ba{\l}aban, Tadeusz},
  title = {{Regularity and decay of lattice Green's functions}},
  journal = {Communications in Mathematical Physics},
  volume = {89},
  number = {4},
  pages = {571--597},
  year = {1983},
  doi = {10.1007/BF01214744},
  url = {https://doi.org/10.1007/BF01214744},
}

@article{Balaban1987RGI,
  author = {Ba{\l}aban, Tadeusz},
  title = {{Renormalization group approach to lattice gauge field theories. I. Generation of effective actions in a small field approximation and a coupling constant renormalization in four dimensions}},
  journal = {Communications in Mathematical Physics},
  volume = {109},
  number = {2},
  pages = {249--301},
  year = {1987},
  doi = {10.1007/BF01215223},
  url = {https://doi.org/10.1007/BF01215223},
}

@article{Balaban1989LargeI,
  author = {Ba{\l}aban, Tadeusz},
  title = {{Large field renormalization. I. The basic step of the R operation}},
  journal = {Communications in Mathematical Physics},
  volume = {122},
  number = {2},
  pages = {175--202},
  year = {1989},
  doi = {10.1007/BF01257412},
  url = {https://doi.org/10.1007/BF01257412},
}

@article{Balaban1989LargeII,
  author = {Ba{\l}aban, Tadeusz},
  title = {{Large field renormalization. II. Localization, exponentiation, and bounds for the R operation}},
  journal = {Communications in Mathematical Physics},
  volume = {122},
  number = {3},
  pages = {355--392},
  year = {1989},
  doi = {10.1007/BF01238433},
  url = {https://doi.org/10.1007/BF01238433},
}

@article{Dimock2013Large,
  author = {Dimock, Jonathan},
  title = {{The renormalization group according to Balaban. II. Large fields}},
  journal = {Journal of Mathematical Physics},
  volume = {54},
  number = {9},
  pages = {092301},
  year = {2013},
  doi = {10.1063/1.4821275},
  eprint = {1212.5562},
  archivePrefix = {arXiv},
  primaryClass = {math-ph},
  url = {https://doi.org/10.1063/1.4821275},
}

@article{Dimock2014Convergence,
  author = {Dimock, Jonathan},
  title = {{The Renormalization Group According to Balaban III. Convergence}},
  journal = {Annales Henri Poincar{\'e}},
  volume = {15},
  number = {11},
  pages = {2133--2175},
  year = {2014},
  doi = {10.1007/s00023-013-0303-3},
  eprint = {1304.0705},
  archivePrefix = {arXiv},
  primaryClass = {math-ph},
  url = {https://doi.org/10.1007/s00023-013-0303-3},
}

@article{Dimock2015Axial,
  author = {Dimock, Jonathan},
  title = {{Covariant Axial Gauge}},
  journal = {Letters in Mathematical Physics},
  volume = {105},
  number = {7},
  pages = {959--987},
  year = {2015},
  doi = {10.1007/s11005-015-0763-0},
  eprint = {1410.2798},
  archivePrefix = {arXiv},
  primaryClass = {math-ph},
  url = {https://doi.org/10.1007/s11005-015-0763-0},
}

@article{FernandezProcacci2007,
  author = {Fern{\'a}ndez, Roberto and Procacci, Aldo},
  title = {{Cluster Expansion for Abstract Polymer Models. New Bounds from an Old Approach}},
  journal = {Communications in Mathematical Physics},
  volume = {274},
  number = {1},
  pages = {123--140},
  year = {2007},
  doi = {10.1007/s00220-007-0279-2},
  eprint = {math-ph/0605041},
  archivePrefix = {arXiv},
  primaryClass = {math-ph},
  url = {https://doi.org/10.1007/s00220-007-0279-2},
}

@article{CombesThomas1973,
  author = {Combes, Jean-Michel and Thomas, Lawrence},
  title = {{Asymptotic Behaviour of Eigenfunctions for Multiparticle {Schr{\"o}dinger} Operators}},
  journal = {Communications in Mathematical Physics},
  volume = {34},
  number = {4},
  pages = {251--270},
  year = {1973},
  doi = {10.1007/BF01646473},
  url = {https://doi.org/10.1007/BF01646473},
}

@article{Gross1975,
  author = {Gross, Leonard},
  title = {{Logarithmic Sobolev Inequalities}},
  journal = {American Journal of Mathematics},
  volume = {97},
  number = {4},
  pages = {1061--1083},
  year = {1975},
  doi = {10.2307/2373688},
  url = {https://doi.org/10.2307/2373688},
}

@article{BrascampLieb1976,
  author = {Brascamp, Herm Jan and Lieb, Elliott H.},
  title = {{On Extensions of the {Brunn--Minkowski} and {Pr{\'e}kopa--Leindler} Theorems, Including Inequalities for Log Concave Functions, and with an Application to the Diffusion Equation}},
  journal = {Journal of Functional Analysis},
  volume = {22},
  number = {4},
  pages = {366--389},
  year = {1976},
  doi = {10.1016/0022-1236(76)90004-5},
  url = {https://doi.org/10.1016/0022-1236(76)90004-5},
}

@incollection{BakryEmery1985,
  author = {Bakry, Dominique and {\'E}mery, Michel},
  title = {{Diffusions hypercontractives}},
  booktitle = {{S{\'e}minaire de Probabilit{\'e}s {XIX} 1983/84}},
  series = {Lecture Notes in Mathematics},
  volume = {1123},
  pages = {177--206},
  publisher = {Springer},
  year = {1985},
  doi = {10.1007/BFb0075847},
  url = {https://www.numdam.org/item/SPS_1985__19__177_0/},
}

@article{HelfferSjostrand1994,
  author = {Helffer, Bernard and Sj{\"o}strand, Johannes},
  title = {{On the Correlation for Kac-like Models in the Convex Case}},
  journal = {Journal of Statistical Physics},
  volume = {74},
  number = {1--2},
  pages = {349--409},
  year = {1994},
  doi = {10.1007/BF02186817},
  url = {https://doi.org/10.1007/BF02186817},
}

@incollection{Ledoux1999,
  author = {Ledoux, Michel},
  title = {{Concentration of Measure and Logarithmic Sobolev Inequalities}},
  booktitle = {{S{\'e}minaire de Probabilit{\'e}s {XXXIII}}},
  series = {Lecture Notes in Mathematics},
  volume = {1709},
  pages = {120--216},
  publisher = {Springer},
  year = {1999},
  doi = {10.1007/BFb0096511},
  url = {https://www.numdam.org/item/SPS_1999__33__120_0/},
}

@article{Adamczak2015,
  author = {Adamczak, Rados{\l}aw},
  title = {{A Note on the {Hanson--Wright} Inequality for Random Vectors with Dependencies}},
  journal = {Electronic Communications in Probability},
  volume = {20},
  number = {72},
  pages = {1--13},
  year = {2015},
  doi = {10.1214/ECP.v20-3829},
  eprint = {1409.8457},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1409.8457},
}

@article{HansonWright1971,
  author = {Hanson, D. L. and Wright, F. T.},
  title = {{A Bound on Tail Probabilities for Quadratic Forms in Independent Random Variables}},
  journal = {The Annals of Mathematical Statistics},
  volume = {42},
  number = {3},
  pages = {1079--1083},
  year = {1971},
  doi = {10.1214/aoms/1177693335},
  url = {https://doi.org/10.1214/aoms/1177693335},
}

@book{Bhatia1997,
  author = {Bhatia, Rajendra},
  title = {{Matrix Analysis}},
  series = {Graduate Texts in Mathematics},
  volume = {169},
  publisher = {Springer},
  address = {New York},
  year = {1997},
  doi = {10.1007/978-1-4612-0653-8},
  url = {https://doi.org/10.1007/978-1-4612-0653-8},
}

@article{Helffer1998,
  author = {Helffer, Bernard},
  title = {{Remarks on Decay of Correlations and Witten Laplacians: {Brascamp--Lieb} Inequalities and Semiclassical Limit}},
  journal = {Journal of Functional Analysis},
  volume = {155},
  number = {2},
  pages = {571--586},
  year = {1998},
  doi = {10.1006/jfan.1997.3239},
  url = {https://doi.org/10.1006/jfan.1997.3239},
}

@article{CCHeat2022v4,
  author = {Cao, Sky and Chatterjee, Sourav},
  title = {The {Yang--Mills} Heat Flow with Random Distributional Initial Data},
  journal = {Communications in Partial Differential Equations},
  volume = {48},
  number = {2},
  pages = {209--251},
  year = {2023},
  doi = {10.1080/03605302.2023.2169937},
  eprint = {2111.10652v4},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/2111.10652v4},
  note = {All numbered and printed-page locators refer to arXiv:2111.10652v4, 25 August 2022, not journal pagination. Only deterministic smooth-data results are used: Theorem 1.2 and Lemma 1.3, p. 3; Lemmas C.2--C.3, pp. 55--56; Corollary C.6, p. 58; Lemmas C.12--C.13, p. 61},
}

@article{CCState2023v4,
  author = {Cao, Sky and Chatterjee, Sourav},
  title = {A State Space for {3D} Euclidean {Yang--Mills} Theories},
  journal = {Communications in Mathematical Physics},
  volume = {405},
  number = {1},
  pages = {3},
  year = {2024},
  doi = {10.1007/s00220-023-04870-y},
  eprint = {2111.12813v4},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/2111.12813v4},
  note = {Article 3, 69 pp. All numbered and printed-page locators refer to arXiv:2111.12813v4, 20 November 2023, not journal pagination, including Lemmas 1.4--1.5 and Theorem 1.6, p. 7; Theorem 3.14, p. 25; Theorem 3.51, pp. 35--36; Lemma 3.68, p. 40},
}

@article{Zwanziger1981,
  author = {Zwanziger, Daniel},
  title = {{Covariant Quantization of Gauge Fields without {Gribov} Ambiguity}},
  journal = {Nuclear Physics B},
  volume = {192},
  number = {1},
  pages = {259--269},
  year = {1981},
  doi = {10.1016/0550-3213(81)90202-9},
  url = {https://doi.org/10.1016/0550-3213(81)90202-9},
}

@article{Uhlenbeck1982Connections,
  author = {Uhlenbeck, Karen K.},
  title = {{Connections with {$L^p$} Bounds on Curvature}},
  journal = {Communications in Mathematical Physics},
  volume = {83},
  number = {1},
  pages = {31--42},
  year = {1982},
  doi = {10.1007/BF01947069},
  url = {https://doi.org/10.1007/BF01947069},
}

@article{Rade1992,
  author = {R{\aa}de, Johan},
  title = {{On the {Yang--Mills} Heat Equation in Two and Three Dimensions}},
  journal = {Journal f{\"u}r die reine und angewandte Mathematik},
  volume = {431},
  pages = {123--163},
  year = {1992},
  doi = {10.1515/crll.1992.431.123},
  url = {https://doi.org/10.1515/crll.1992.431.123},
  note = {Publisher metadata gives pages 123--164, including a blank final verso; substantive text ends at page 163.},
}

@article{Sengupta1994,
  author = {Sengupta, Ambar},
  title = {{Gauge Invariant Functions of Connections}},
  journal = {Proceedings of the American Mathematical Society},
  volume = {121},
  number = {3},
  pages = {897--905},
  year = {1994},
  doi = {10.1090/S0002-9939-1994-1215205-7},
  url = {https://doi.org/10.1090/S0002-9939-1994-1215205-7},
}

@article{DaPratoDebussche2003,
  author = {Da Prato, Giuseppe and Debussche, Arnaud},
  title = {{Strong Solutions to the Stochastic Quantization Equations}},
  journal = {The Annals of Probability},
  volume = {31},
  number = {4},
  pages = {1900--1916},
  year = {2003},
  doi = {10.1214/aop/1068646370},
  url = {https://doi.org/10.1214/aop/1068646370},
}

@article{Luscher2010WilsonFlow,
  author = {L{\"u}scher, Martin},
  title = {{Properties and Uses of the {Wilson} Flow in Lattice {QCD}}},
  journal = {Journal of High Energy Physics},
  volume = {2010},
  number = {08},
  pages = {071},
  year = {2010},
  doi = {10.1007/JHEP08(2010)071},
  eprint = {1006.4518},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1006.4518},
  note = {Erratum: Journal of High Energy Physics 2014, no. 03, article 092, doi:10.1007/JHEP03(2014)092.},
}

@article{CharalambousGross2013,
  author = {Charalambous, Nelia and Gross, Leonard},
  title = {{The {Yang--Mills} Heat Semigroup on Three-Manifolds with Boundary}},
  journal = {Communications in Mathematical Physics},
  volume = {317},
  number = {3},
  pages = {727--785},
  year = {2013},
  doi = {10.1007/s00220-012-1558-0},
  eprint = {1004.1639},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1004.1639},
}

@article{Chevyrev2019,
  author = {Chevyrev, Ilya},
  title = {{{Yang--Mills} Measure on the Two-Dimensional Torus as a Random Distribution}},
  journal = {Communications in Mathematical Physics},
  volume = {372},
  number = {3},
  pages = {1027--1058},
  year = {2019},
  doi = {10.1007/s00220-019-03567-5},
  eprint = {1808.09196},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1808.09196},
}

@article{ChandraChevyrevHairerShen2022,
  author = {Chandra, Ajay and Chevyrev, Ilya and Hairer, Martin and Shen, Hao},
  title = {{Langevin Dynamic for the {2D Yang--Mills} Measure}},
  journal = {Publications math{\'e}matiques de l'IH{\'E}S},
  volume = {136},
  pages = {1--147},
  year = {2022},
  doi = {10.1007/s10240-022-00132-0},
  eprint = {2006.04987},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2006.04987},
}

@article{ChandraChevyrevHairerShen2024,
  author = {Chandra, Ajay and Chevyrev, Ilya and Hairer, Martin and Shen, Hao},
  title = {{Stochastic Quantisation of {Yang--Mills--Higgs} in {3D}}},
  journal = {Inventiones mathematicae},
  volume = {237},
  number = {2},
  pages = {541--696},
  year = {2024},
  doi = {10.1007/s00222-024-01264-2},
  eprint = {2201.03487},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2201.03487},
}

@article{ChevyrevShen2026Invariant,
  author = {Chevyrev, Ilya and Shen, Hao},
  title = {{Invariant Measure and Universality of the {2D Yang--Mills} Langevin Dynamic}},
  journal = {Communications on Pure and Applied Mathematics},
  volume = {79},
  number = {8},
  pages = {1973--2102},
  year = {2026},
  doi = {10.1002/cpa.70043},
  eprint = {2302.12160v3},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2302.12160v3},
}

@article{ChevyrevShen2026Uniqueness,
  author = {Chevyrev, Ilya and Shen, Hao},
  title = {{Uniqueness of Gauge Covariant Renormalisation of Stochastic {3D Yang--Mills--Higgs}}},
  journal = {Archive for Rational Mechanics and Analysis},
  volume = {250},
  number = {1},
  pages = {11},
  year = {2026},
  doi = {10.1007/s00205-025-02163-3},
  eprint = {2503.03060v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2503.03060v2},
}

@article{DeTurck1983,
  author = {DeTurck, Dennis M.},
  title = {{Deforming Metrics in the Direction of Their {Ricci} Tensors}},
  journal = {Journal of Differential Geometry},
  volume = {18},
  number = {1},
  pages = {157--162},
  year = {1983},
  doi = {10.4310/jdg/1214509286},
  url = {https://doi.org/10.4310/jdg/1214509286},
}

@article{Donaldson1985,
  author = {Donaldson, Simon K.},
  title = {{Anti Self-Dual {Yang--Mills} Connections over Complex Algebraic Surfaces and Stable Vector Bundles}},
  journal = {Proceedings of the London Mathematical Society},
  series = {Third Series},
  volume = {50},
  number = {1},
  pages = {1--26},
  year = {1985},
  doi = {10.1112/plms/s3-50.1.1},
  url = {https://doi.org/10.1112/plms/s3-50.1.1},
}

@article{Chevyrev2022Survey,
  author = {Chevyrev, Ilya},
  title = {{Stochastic Quantization of {Yang--Mills}}},
  journal = {Journal of Mathematical Physics},
  volume = {63},
  number = {9},
  pages = {091101},
  year = {2022},
  doi = {10.1063/5.0089431},
  eprint = {2202.13359},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2202.13359},
}

@article{Horowitz1972Characters,
  author = {Horowitz, Robert D.},
  title = {{Characters of free groups represented in the two-dimensional special linear group}},
  journal = {Communications on Pure and Applied Mathematics},
  volume = {25},
  number = {6},
  pages = {635--649},
  year = {1972},
  doi = {10.1002/cpa.3160250602},
  url = {https://doi.org/10.1002/cpa.3160250602},
}

@article{Luscher1983Torus,
  author = {L{\"u}scher, Martin},
  title = {{Some analytic results concerning the mass spectrum of Yang-Mills gauge theories on a torus}},
  journal = {Nuclear Physics B},
  volume = {219},
  number = {1},
  pages = {233--261},
  year = {1983},
  doi = {10.1016/0550-3213(83)90436-4},
  url = {https://doi.org/10.1016/0550-3213(83)90436-4},
}

@article{CosteEtAl1985ZeroMomentum,
  author = {Coste, A. and Gonz{\'a}lez-Arroyo, Antonio and Jurkiewicz, J. and Korthals Altes, C. P.},
  title = {{Zero-momentum contribution to Wilson loops in periodic boxes}},
  journal = {Nuclear Physics B},
  volume = {262},
  number = {1},
  pages = {67--94},
  year = {1985},
  doi = {10.1016/0550-3213(85)90064-1},
  url = {https://doi.org/10.1016/0550-3213(85)90064-1},
}

@article{KrauthNicolaiStaudacher1998,
  author = {Krauth, Werner and Nicolai, Hermann and Staudacher, Matthias},
  title = {{Monte Carlo approach to M-theory}},
  journal = {Physics Letters B},
  volume = {431},
  number = {1-2},
  pages = {31--41},
  year = {1998},
  doi = {10.1016/S0370-2693(98)00557-7},
  eprint = {hep-th/9803117},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/hep-th/9803117},
}

@article{AustingWheater2001Convergence,
  author = {Austing, Peter and Wheater, John F.},
  title = {{The convergence of Yang-Mills integrals}},
  journal = {Journal of High Energy Physics},
  volume = {2001},
  number = {02},
  pages = {028},
  year = {2001},
  doi = {10.1088/1126-6708/2001/02/028},
  eprint = {hep-th/0101071},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/hep-th/0101071},
}

@book{Wong2001AsymptoticIntegrals,
  author = {Wong, Roderick},
  title = {{Asymptotic Approximations of Integrals}},
  series = {Classics in Applied Mathematics},
  volume = {34},
  publisher = {Society for Industrial and Applied Mathematics},
  year = {2001},
  doi = {10.1137/1.9780898719260},
  url = {https://doi.org/10.1137/1.9780898719260},
  note = {SIAM reprint of the 1989 Academic Press edition.},
}

@article{KrauthStaudacher1998FiniteIntegrals,
  author = {Krauth, Werner and Staudacher, Matthias},
  title = {{Finite Yang-Mills integrals}},
  journal = {Physics Letters B},
  volume = {435},
  number = {3-4},
  pages = {350--355},
  year = {1998},
  doi = {10.1016/S0370-2693(98)00814-4},
  eprint = {hep-th/9804199},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/hep-th/9804199},
}

@article{FodorEtAl2012FiniteVolumeFlow,
  author = {Fodor, Zoltan and Holland, Kieran and Kuti, Julius and Nogradi, Daniel and Wong, Chik Him},
  title = {{The Yang-Mills gradient flow in finite volume}},
  journal = {Journal of High Energy Physics},
  volume = {2012},
  number = {11},
  pages = {007},
  year = {2012},
  doi = {10.1007/JHEP11(2012)007},
  eprint = {1208.1051},
  archivePrefix = {arXiv},
  primaryClass = {hep-lat},
  url = {https://arxiv.org/abs/1208.1051},
}

@article{Bott1954CriticalManifolds,
  author = {Bott, Raoul},
  title = {{Nondegenerate critical manifolds}},
  journal = {Annals of Mathematics},
  volume = {60},
  number = {2},
  pages = {248--261},
  year = {1954},
  doi = {10.2307/1969631},
  url = {https://doi.org/10.2307/1969631},
}

@article{Dudley1967,
  author = {Dudley, Richard M.},
  title = {{The Sizes of Compact Subsets of {Hilbert} Space and Continuity of {Gaussian} Processes}},
  journal = {Journal of Functional Analysis},
  volume = {1},
  number = {3},
  pages = {290--330},
  year = {1967},
  doi = {10.1016/0022-1236(67)90017-1},
  url = {https://doi.org/10.1016/0022-1236(67)90017-1},
}

@incollection{Stein1972NormalApproximation,
  author = {Stein, Charles},
  title = {{A bound for the error in the normal approximation to the distribution of a sum of dependent random variables}},
  editor = {Le Cam, Lucien M. and Neyman, Jerzy and Scott, Elizabeth L.},
  booktitle = {{Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume II: Probability Theory}},
  pages = {583--602},
  publisher = {University of California Press},
  year = {1972},
  url = {https://digicoll.lib.berkeley.edu/record/113245},
}

@article{Borell1975GaussianIsoperimetry,
  author = {Borell, Christer},
  title = {{The Brunn-Minkowski inequality in Gauss space}},
  journal = {Inventiones Mathematicae},
  volume = {30},
  number = {2},
  pages = {207--216},
  year = {1975},
  doi = {10.1007/BF01425510},
  url = {https://doi.org/10.1007/BF01425510},
}

@incollection{CirelsonIbragimovSudakov1976,
  author = {Cirel'son, B. S. and Ibragimov, I. A. and Sudakov, V. N.},
  title = {{Norms of Gaussian sample functions}},
  editor = {Maruyama, Gisiro and Prokhorov, Jurii V.},
  booktitle = {{Proceedings of the Third Japan--USSR Symposium on Probability Theory}},
  series = {Lecture Notes in Mathematics},
  volume = {550},
  pages = {20--41},
  publisher = {Springer},
  year = {1976},
  doi = {10.1007/BFb0077482},
  url = {https://doi.org/10.1007/BFb0077482},
}

@article{Dirksen2015,
  author = {Dirksen, Sjoerd},
  title = {{Tail Bounds via Generic Chaining}},
  journal = {Electronic Journal of Probability},
  volume = {20},
  number = {53},
  pages = {1--29},
  year = {2015},
  doi = {10.1214/EJP.v20-3760},
  eprint = {1309.3522},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1309.3522},
}

@article{Isserlis1918GaussianMoments,
  author = {Isserlis, Leon},
  title = {{On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables}},
  journal = {Biometrika},
  volume = {12},
  number = {1-2},
  pages = {134--139},
  year = {1918},
  doi = {10.1093/biomet/12.1-2.134},
  url = {https://doi.org/10.1093/biomet/12.1-2.134},
}

@article{SudakovTsirelson1974GaussianIsoperimetry,
  author = {Sudakov, V. N. and Tsirel'son, B. S.},
  title = {{Extremal properties of half-spaces for spherically invariant measures}},
  journal = {Journal of Soviet Mathematics},
  volume = {9},
  number = {1},
  pages = {9--18},
  year = {1978},
  doi = {10.1007/BF01086099},
  url = {https://doi.org/10.1007/BF01086099},
  note = {English translation. Russian original: Zapiski Nauchnykh Seminarov LOMI 41 (1974), 14--24, 165.},
}

@book{AdlerTaylor2007,
  author = {Adler, Robert J. and Taylor, Jonathan E.},
  title = {Random Fields and Geometry},
  series = {Springer Monographs in Mathematics},
  publisher = {Springer},
  address = {New York},
  year = {2007},
  isbn = {978-0-387-48112-8},
  doi = {10.1007/978-0-387-48116-6},
  url = {https://doi.org/10.1007/978-0-387-48116-6},
  note = {Theorem 2.1.1, printed p. 50, (2.1.5); Lemma 2.1.5, printed p. 54, (2.1.13), proof pp. 54--55. Used with the authors' correction list of 7 October 2015, entries 54-6, 55-11, and 55-4: \url{https://robert.net.technion.ac.il/files/2016/08/corrections.pdf}. Gaussian reference only},
}

@book{Seiler1982,
  author = {Seiler, Erhard},
  title = {Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics},
  year = {1982},
  publisher = {Springer},
  series = {Lecture Notes in Physics},
  volume = {159},
  doi = {10.1007/3-540-11559-5},
  url = {https://link.springer.com/book/10.1007/3-540-11559-5},
}

@article{Brydges1979a,
  author = {Brydges, David and Fr{\"o}hlich, J{\"u}rg and Seiler, Erhard},
  title = {Diamagnetic and critical properties of {Higgs} lattice gauge theories},
  year = {1979},
  journal = {Nuclear Physics B},
  volume = {152},
  number = {3--4},
  pages = {521--532},
  doi = {10.1016/0550-3213(79)90095-6},
  url = {https://www.sciencedirect.com/science/article/pii/0550321379900956},
}

@article{Brydges1979b,
  author = {Brydges, David and Fr{\"o}hlich, J{\"u}rg and Seiler, Erhard},
  title = {On the construction of quantized gauge fields. {I}. General results},
  year = {1979},
  journal = {Annals of Physics},
  volume = {121},
  number = {1--2},
  pages = {227--284},
  doi = {10.1016/0003-4916(79)90098-8},
  url = {https://www.sciencedirect.com/science/article/abs/pii/0003491679900988},
}

@article{Brydges1980,
  author = {Brydges, David C. and Fr{\"o}hlich, J{\"u}rg and Seiler, Erhard},
  title = {Construction of quantised gauge fields. {II}. Convergence of the lattice approximation},
  year = {1980},
  journal = {Communications in Mathematical Physics},
  volume = {71},
  number = {2},
  pages = {159--205},
  doi = {10.1007/BF01197918},
  url = {https://link.springer.com/article/10.1007/BF01197918},
}

@article{Brydges1981,
  author = {Brydges, David C. and Fr{\"o}hlich, J{\"u}rg and Seiler, Erhard},
  title = {On the construction of quantized gauge fields. {III}. The two-dimensional abelian {Higgs} model without cutoffs},
  year = {1981},
  journal = {Communications in Mathematical Physics},
  volume = {79},
  number = {3},
  pages = {353--399},
  doi = {10.1007/BF01208500},
  url = {https://link.springer.com/article/10.1007/BF01208500},
}

@article{King1986a,
  author = {King, Christopher},
  title = {The {U(1) Higgs} model. {I}. The continuum limit},
  year = {1986},
  journal = {Communications in Mathematical Physics},
  volume = {102},
  number = {4},
  pages = {649--677},
  doi = {10.1007/BF01221651},
  url = {https://link.springer.com/article/10.1007/BF01221651},
}

@article{King1986b,
  author = {King, Christopher},
  title = {The {U(1) Higgs} model. {II}. The infinite volume limit},
  year = {1986},
  journal = {Communications in Mathematical Physics},
  volume = {103},
  number = {2},
  pages = {323--349},
  doi = {10.1007/BF01206942},
  url = {https://link.springer.com/article/10.1007/BF01206942},
}

@incollection{Balaban1984d,
  author = {Ba{\l}aban, Tadeusz and Imbrie, John and Jaffe, Arthur},
  title = {Exact Renormalization Group for Gauge Theories},
  year = {1984},
  booktitle = {Progress in Gauge Field Theory},
  publisher = {Plenum Press},
  series = {NATO ASI Series B},
  volume = {115},
  pages = {79--103},
  doi = {10.1007/978-1-4757-0280-4_4},
  url = {https://link.springer.com/chapter/10.1007/978-1-4757-0280-4_4},
}

@article{Balaban1985f,
  author = {Ba{\l}aban, Tadeusz and Imbrie, John and Jaffe, Arthur},
  title = {Renormalization of the {Higgs} model: Minimizers, propagators and the stability of mean field theory},
  year = {1985},
  journal = {Communications in Mathematical Physics},
  volume = {97},
  number = {1--2},
  pages = {299--329},
  doi = {10.1007/BF01206191},
  url = {https://link.springer.com/article/10.1007/BF01206191},
}

@incollection{BalabanJaffe1986,
  author = {Ba{\l}aban, Tadeusz and Jaffe, Arthur},
  title = {Constructive Gauge Theory},
  year = {1986},
  booktitle = {Fundamental Problems of Gauge Field Theory},
  publisher = {Plenum Press},
  series = {NATO ASI Series B},
  volume = {141},
  pages = {207--263},
  doi = {10.1007/978-1-4757-0363-4_5},
  url = {https://link.springer.com/chapter/10.1007/978-1-4757-0363-4_5},
}

@article{Balaban1988c,
  author = {Ba{\l}aban, Tadeusz and Imbrie, John Z. and Jaffe, Arthur},
  title = {Effective action and cluster properties of the abelian {Higgs} model},
  year = {1988},
  journal = {Communications in Mathematical Physics},
  volume = {114},
  number = {2},
  pages = {257--315},
  doi = {10.1007/BF01225038},
  url = {https://link.springer.com/article/10.1007/BF01225038},
}

@article{Federbush1986,
  author = {Federbush, Paul},
  title = {A phase cell approach to {Yang--Mills} theory. {I}. Modes, lattice-continuum duality},
  year = {1986},
  journal = {Communications in Mathematical Physics},
  volume = {107},
  number = {2},
  pages = {319--329},
  doi = {10.1007/BF01209397},
  url = {https://link.springer.com/article/10.1007/BF01209397},
}

@article{Federbush1987a,
  author = {Federbush, Paul},
  title = {A phase cell approach to {Yang--Mills} theory. {III}. Local stability, modified renormalization group transformation},
  year = {1987},
  journal = {Communications in Mathematical Physics},
  volume = {110},
  number = {2},
  pages = {293--309},
  doi = {10.1007/BF01207369},
  url = {https://link.springer.com/article/10.1007/BF01207369},
}

@article{Federbush1987b,
  author = {Federbush, Paul},
  title = {A phase cell approach to {Yang--Mills} theory. {VI}. Non-abelian lattice-continuum duality},
  year = {1987},
  journal = {Annales de l'Institut Henri Poincar{\'e}, Physique th{\'e}orique},
  volume = {47},
  number = {1},
  pages = {17--23},
  url = {https://www.numdam.org/item/AIHPA_1987__47_1_17_0/},
  note = {Bibliographic record verified in Numdam; no DOI or arXiv identifier located.},
}

@article{FederbushWilliamson1987,
  author = {Federbush, Paul and Williamson, Calvin},
  title = {A phase cell approach to {Yang--Mills} theory. {II}. Analysis of a mode},
  year = {1987},
  journal = {Journal of Mathematical Physics},
  volume = {28},
  number = {6},
  pages = {1416--1419},
  url = {https://pubs.aip.org/aip/jmp/issue/28/6},
  doi = {10.1063/1.527495},
}

@article{Federbush1988,
  author = {Federbush, Paul},
  title = {A phase cell approach to {Yang--Mills} theory. {IV}. The choice of variables},
  year = {1988},
  journal = {Communications in Mathematical Physics},
  volume = {114},
  number = {2},
  pages = {317--343},
  doi = {10.1007/BF01225039},
  url = {https://link.springer.com/article/10.1007/BF01225039},
}

@article{Federbush1990,
  author = {Federbush, Paul},
  title = {A phase cell approach to {Yang--Mills} theory. {V}. Analysis of a chunk},
  year = {1990},
  journal = {Communications in Mathematical Physics},
  volume = {127},
  number = {3},
  pages = {433--457},
  doi = {10.1007/BF02104497},
  url = {https://link.springer.com/article/10.1007/BF02104497},
}

@article{GawedzkiKupiainen1980,
  author = {Gaw{\k{e}}dzki, Krzysztof and Kupiainen, Antti},
  title = {A rigorous block spin approach to massless lattice theories},
  year = {1980},
  journal = {Communications in Mathematical Physics},
  volume = {77},
  number = {1},
  pages = {31--64},
  doi = {10.1007/BF01205038},
  url = {https://link.springer.com/article/10.1007/BF01205038},
}

@article{GawedzkiKupiainen1983a,
  author = {Gaw{\k{e}}dzki, Krzysztof and Kupiainen, Antti},
  title = {Block spin renormalization group for dipole gas and $(\nabla\varphi)^4$},
  year = {1983},
  journal = {Annals of Physics},
  volume = {147},
  number = {1},
  pages = {198--243},
  doi = {10.1016/0003-4916(83)90071-4},
  url = {https://www.sciencedirect.com/science/article/pii/0003491683900714},
}

@incollection{GawedzkiKupiainen1983b,
  author = {Gaw{\k{e}}dzki, Krzysztof and Kupiainen, Antti},
  title = {Rigorous Renormalization Group and Asymptotic Freedom},
  year = {1983},
  booktitle = {Scaling and Self-Similarity in Physics},
  publisher = {Birkh{\"a}user},
  series = {Progress in Physics},
  volume = {7},
  pages = {227--262},
  doi = {10.1007/978-1-4899-6762-6_7},
  url = {https://link.springer.com/chapter/10.1007/978-1-4899-6762-6_7},
}

@article{GawedzkiKupiainen1986,
  author = {Gaw{\k{e}}dzki, Krzysztof and Kupiainen, Antti},
  title = {Continuum limit of the hierarchical {$O(N)$} non-linear $\sigma$-model},
  year = {1986},
  journal = {Communications in Mathematical Physics},
  volume = {106},
  number = {4},
  pages = {533--550},
  doi = {10.1007/BF01463394},
  url = {https://link.springer.com/article/10.1007/BF01463394},
}

@incollection{Brydges2009,
  author = {Brydges, David C.},
  title = {Lectures on the renormalisation group},
  year = {2009},
  booktitle = {Statistical Mechanics},
  series = {IAS/Park City Mathematics Series},
  volume = {16},
  publisher = {American Mathematical Society},
  pages = {7--93},
  editor = {Sheffield, Scott and Spencer, Thomas},
  doi = {10.1090/pcms/016/02},
  url = {https://doi.org/10.1090/pcms/016/02},
}

@article{Dimock2015b,
  author = {Dimock, Jonathan},
  title = {Nonperturbative renormalization of scalar quantum electrodynamics in {$d=3$}},
  year = {2015},
  journal = {Journal of Mathematical Physics},
  volume = {56},
  number = {10},
  pages = {102304},
  doi = {10.1063/1.4933224},
  eprint = {1502.02946},
  archivePrefix = {arXiv},
  url = {https://pubs.aip.org/aip/jmp/issue/56/10},
}

@article{Dimock2018,
  author = {Dimock, Jonathan},
  title = {Ultraviolet regularity for {QED} in {$d=3$}},
  year = {2018},
  journal = {Journal of Mathematical Physics},
  volume = {59},
  number = {1},
  pages = {012301},
  doi = {10.1063/1.5009458},
  eprint = {1512.04373},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1512.04373},
}

@article{Dimock2020,
  author = {Dimock, Jonathan},
  title = {Multiscale block averaging for {QED} in {$d=3$}},
  year = {2020},
  journal = {Journal of Mathematical Physics},
  volume = {61},
  number = {3},
  pages = {032302},
  doi = {10.1063/1.5134439},
  eprint = {1712.10029},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1712.10029},
}

@book{GlimmJaffe1987,
  author = {Glimm, James and Jaffe, Arthur},
  title = {Quantum Physics: A Functional Integral Point of View},
  year = {1987},
  publisher = {Springer},
  edition = {2},
  doi = {10.1007/978-1-4612-4728-9},
  url = {https://link.springer.com/book/10.1007/978-1-4612-4728-9},
}

@book{Rivasseau1991,
  author = {Rivasseau, Vincent},
  title = {From Perturbative to Constructive Renormalization},
  year = {1991},
  publisher = {Princeton University Press},
  series = {Princeton Series in Physics},
  note = {Originally published in 1991; DOI refers to the electronic reissue (2014).},
  doi = {10.1515/9781400862085},
  url = {https://www.degruyterbrill.com/document/doi/10.1515/9781400862085/html},
}

@incollection{JaffeWitten2006,
  author = {Jaffe, Arthur and Witten, Edward},
  title = {Quantum {Yang--Mills} Theory},
  year = {2006},
  booktitle = {The Millennium Prize Problems},
  publisher = {Clay Mathematics Institute and American Mathematical Society},
  pages = {129--152},
  editor = {Carlson, James and Jaffe, Arthur and Wiles, Andrew},
  url = {https://www.claymath.org/wp-content/uploads/2022/06/yangmills.pdf},
  note = {Published version, pp. 129--152; official Clay PDF also available. No chapter DOI or arXiv identifier verified.},
}

@article{Douglas2026,
  author = {Douglas, Michael R.},
  title = {The {Yang--Mills} Millennium problem},
  year = {2026},
  journal = {Nature Reviews Physics},
  volume = {8},
  number = {2},
  pages = {86--97},
  doi = {10.1038/s42254-025-00909-2},
  url = {https://www.nature.com/articles/s42254-025-00909-2},
}

@article{Gross1989,
  author = {Gross, Leonard and King, Christopher and Sengupta, Ambar},
  title = {Two dimensional {Yang--Mills} theory via stochastic differential equations},
  journal = {Annals of Physics},
  volume = {194},
  number = {1},
  pages = {65--112},
  year = {1989},
  doi = {10.1016/0003-4916(89)90032-8},
  url = {https://doi.org/10.1016/0003-4916(89)90032-8},
}

@article{Driver1989,
  author = {Driver, Bruce K.},
  title = {{YM}$_2$: Continuum expectations, lattice convergence, and lassos},
  journal = {Communications in Mathematical Physics},
  volume = {123},
  number = {4},
  pages = {575--616},
  year = {1989},
  doi = {10.1007/BF01218586},
  url = {https://doi.org/10.1007/BF01218586},
}

@article{Fine1990,
  author = {Fine, Dana S.},
  title = {Quantum {Yang--Mills} on the two-sphere},
  journal = {Communications in Mathematical Physics},
  volume = {134},
  number = {2},
  pages = {273--292},
  year = {1990},
  doi = {10.1007/BF02097703},
  url = {https://doi.org/10.1007/BF02097703},
}

@article{Fine1991,
  author = {Fine, Dana S.},
  title = {Quantum {Yang--Mills} on a {Riemann} surface},
  journal = {Communications in Mathematical Physics},
  volume = {140},
  number = {2},
  pages = {321--338},
  year = {1991},
  doi = {10.1007/BF02099502},
  url = {https://doi.org/10.1007/BF02099502},
}

@article{Witten1991,
  author = {Witten, Edward},
  title = {On quantum gauge theories in two dimensions},
  journal = {Communications in Mathematical Physics},
  volume = {141},
  number = {1},
  pages = {153--209},
  year = {1991},
  doi = {10.1007/BF02100009},
  url = {https://doi.org/10.1007/BF02100009},
}

@article{Sengupta1992,
  author = {Sengupta, Ambar},
  title = {The {Yang--Mills} measure for {$S^2$}},
  journal = {Journal of Functional Analysis},
  volume = {108},
  number = {2},
  pages = {231--273},
  year = {1992},
  doi = {10.1016/0022-1236(92)90025-E},
  url = {https://doi.org/10.1016/0022-1236(92)90025-E},
}

@article{Sengupta1993,
  author = {Sengupta, Ambar},
  title = {Quantum gauge theory on compact surfaces},
  journal = {Annals of Physics},
  volume = {221},
  number = {1},
  pages = {17--52},
  year = {1993},
  doi = {10.1006/aphy.1993.1002},
  url = {https://doi.org/10.1006/aphy.1993.1002},
}

@article{Sengupta1997,
  author = {Sengupta, Ambar},
  title = {Gauge theory on compact surfaces},
  journal = {Memoirs of the American Mathematical Society},
  volume = {126},
  number = {600},
  pages = {viii+85},
  year = {1997},
  doi = {10.1090/memo/0600},
  url = {https://doi.org/10.1090/memo/0600},
}

@article{Levy2003,
  author = {L{\'e}vy, Thierry},
  title = {{Yang--Mills} measure on compact surfaces},
  journal = {Memoirs of the American Mathematical Society},
  volume = {166},
  number = {790},
  pages = {xiv+122},
  year = {2003},
  doi = {10.1090/memo/0790},
  eprint = {math/0101239},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1090/memo/0790},
}

@article{Levy2010,
  author = {L{\'e}vy, Thierry},
  title = {Two-dimensional {Markovian} holonomy fields},
  journal = {Ast{\'e}risque},
  volume = {329},
  pages = {vi+172},
  year = {2010},
  eprint = {0804.2230},
  archivePrefix = {arXiv},
  url = {https://www.numdam.org/item/AST_2010__329__R1_0/},
}

@article{ParisiWu1981,
  author = {Parisi, Giorgio and Wu, Yong-shi},
  title = {Perturbation theory without gauge fixing},
  journal = {Scientia Sinica},
  volume = {24},
  number = {4},
  pages = {483--496},
  year = {1981},
  url = {https://chimera.roma1.infn.it/GIORGIO/papers.html},
}

@article{Bourgain1996,
  author = {Bourgain, Jean},
  title = {Invariant measures for the {2D}-defocusing nonlinear {Schr{\"o}dinger} equation},
  journal = {Communications in Mathematical Physics},
  volume = {176},
  number = {2},
  pages = {421--445},
  year = {1996},
  doi = {10.1007/BF02099556},
  url = {https://doi.org/10.1007/BF02099556},
}

@article{Hairer2014,
  author = {Hairer, Martin},
  title = {A theory of regularity structures},
  journal = {Inventiones mathematicae},
  volume = {198},
  number = {2},
  pages = {269--504},
  year = {2014},
  doi = {10.1007/s00222-014-0505-4},
  eprint = {1303.5113},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1007/s00222-014-0505-4},
}

@article{BringmannCao2026,
  author = {Bringmann, Bjoern and Cao, Sky},
  title = {A para-controlled approach to the stochastic {Yang--Mills} equation in two dimensions},
  journal = {Memoirs of the American Mathematical Society},
  volume = {319},
  number = {1624},
  pages = {v+125},
  year = {2026},
  doi = {10.1090/memo/1624},
  eprint = {2305.07197},
  note = {Publication metadata corroborated by the zbMATH-linked record DE 8212947 and author publication lists; direct AMS page inaccessible during verification.},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1090/memo/1624},
}

@article{CharalambousGross2015,
  author = {Charalambous, Nelia and Gross, Leonard},
  title = {Neumann domination for the {Yang--Mills} heat equation},
  journal = {Journal of Mathematical Physics},
  volume = {56},
  number = {7},
  pages = {073505},
  year = {2015},
  doi = {10.1063/1.4927250},
  eprint = {1405.6496},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1063/1.4927250},
}

@article{CharalambousGross2017,
  author = {Charalambous, Nelia and Gross, Leonard},
  title = {Initial behavior of solutions to the {Yang--Mills} heat equation},
  journal = {Journal of Mathematical Analysis and Applications},
  volume = {451},
  number = {2},
  pages = {873--905},
  year = {2017},
  doi = {10.1016/j.jmaa.2017.02.027},
  eprint = {1609.05607},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1016/j.jmaa.2017.02.027},
}

@article{Gross2022,
  author = {Gross, Leonard},
  title = {The {Yang--Mills} heat equation with finite action in three dimensions},
  journal = {Memoirs of the American Mathematical Society},
  volume = {275},
  number = {1349},
  pages = {v+111},
  year = {2022},
  doi = {10.1090/memo/1349},
  eprint = {1606.04151},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1090/memo/1349},
}

@article{Chatterjee2019a,
  author = {Chatterjee, Sourav},
  title = {Rigorous solution of strongly coupled {$SO(N)$} lattice gauge theory in the large {$N$} limit},
  journal = {Communications in Mathematical Physics},
  volume = {366},
  number = {1},
  pages = {203--268},
  year = {2019},
  doi = {10.1007/s00220-019-03353-3},
  eprint = {1502.07719},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1007/s00220-019-03353-3},
}

@misc{ChatterjeeJafarov2016,
  author = {Chatterjee, Sourav and Jafarov, Jafar},
  title = {The {$1/N$} expansion for {$SO(N)$} lattice gauge theory at strong coupling},
  year = {2016},
  eprint = {1604.04777},
  note = {Preprint; no published version verified.},
  archivePrefix = {arXiv},
  url = {https://inspirehep.net/literature/1448303},
}

@article{BasuGanguly2018,
  author = {Basu, Riddhipratim and Ganguly, Shirshendu},
  title = {{$SO(N)$} lattice gauge theory, planar and beyond},
  journal = {Communications on Pure and Applied Mathematics},
  volume = {71},
  number = {10},
  pages = {2016--2064},
  year = {2018},
  doi = {10.1002/cpa.21788},
  eprint = {1608.04379},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1002/cpa.21788},
}

@article{Shen2023,
  author = {Shen, Hao and Zhu, Rongchan and Zhu, Xiangchan},
  title = {A stochastic analysis approach to lattice {Yang--Mills} at strong coupling},
  journal = {Communications in Mathematical Physics},
  volume = {400},
  number = {2},
  pages = {805--851},
  year = {2023},
  doi = {10.1007/s00220-022-04609-1},
  eprint = {2204.12737},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1007/s00220-022-04609-1},
}

@article{AdhikariCao2025,
  author = {Adhikari, Arka and Cao, Sky},
  title = {Correlation decay for finite lattice gauge theories at weak coupling},
  journal = {The Annals of Probability},
  volume = {53},
  number = {1},
  pages = {140--174},
  year = {2025},
  doi = {10.1214/24-AOP1702},
  eprint = {2202.10375},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1214/24-AOP1702},
}

@misc{CaoNissim2025a,
  author = {Cao, Sky and Nissim, Ron and Sheffield, Scott},
  title = {Expanded regimes of area law for lattice {Yang--Mills} theories},
  year = {2025},
  eprint = {2505.16585},
  note = {Preprint; no published version verified.},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2505.16585},
}

@article{AtiyahBott1983,
  author = {Atiyah, Michael F. and Bott, Raoul},
  title = {The {Yang--Mills} equations over {Riemann} surfaces},
  journal = {Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences},
  volume = {308},
  number = {1505},
  pages = {523--615},
  year = {1983},
  doi = {10.1098/rsta.1983.0017},
  url = {https://doi.org/10.1098/rsta.1983.0017},
}

@article{Donaldson1983,
  author = {Donaldson, Simon K.},
  title = {A new proof of a theorem of {Narasimhan} and {Seshadri}},
  journal = {Journal of Differential Geometry},
  volume = {18},
  number = {2},
  pages = {269--277},
  year = {1983},
  doi = {10.4310/jdg/1214437664},
  url = {https://doi.org/10.4310/jdg/1214437664},
}

@article{NarayananNeuberger2006,
  author = {Narayanan, Rajamani and Neuberger, Herbert},
  title = {Infinite {$N$} phase transitions in continuum {Wilson} loop operators},
  journal = {Journal of High Energy Physics},
  volume = {2006},
  number = {03},
  pages = {064},
  year = {2006},
  doi = {10.1088/1126-6708/2006/03/064},
  eprint = {hep-th/0601210},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1088/1126-6708/2006/03/064},
}

@article{Luscher2010a,
  author = {L{\"u}scher, Martin},
  title = {Trivializing maps, the {Wilson} flow and the {HMC} algorithm},
  journal = {Communications in Mathematical Physics},
  volume = {293},
  number = {3},
  pages = {899--919},
  year = {2010},
  doi = {10.1007/s00220-009-0953-7},
  eprint = {0907.5491},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1007/s00220-009-0953-7},
}

@article{LuscherWeisz2011,
  author = {L{\"u}scher, Martin and Weisz, Peter},
  title = {Perturbative analysis of the gradient flow in non-abelian gauge theories},
  journal = {Journal of High Energy Physics},
  volume = {2011},
  number = {02},
  pages = {051},
  year = {2011},
  doi = {10.1007/JHEP02(2011)051},
  eprint = {1101.0963},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1007/JHEP02(2011)051},
}

@article{GrossWilczek1973,
  author = {Gross, David J. and Wilczek, Frank},
  title = {Ultraviolet Behavior of Non-Abelian Gauge Theories},
  journal = {Physical Review Letters}, volume = {30}, number = {26},
  pages = {1343--1346}, year = {1973}, doi = {10.1103/PhysRevLett.30.1343}
}

@article{Politzer1973,
  author = {Politzer, H. David},
  title = {Reliable Perturbative Results for Strong Interactions?},
  journal = {Physical Review Letters}, volume = {30}, number = {26},
  pages = {1346--1349}, year = {1973}, doi = {10.1103/PhysRevLett.30.1346}
}

@article{Ginsparg1980,
  author = {Ginsparg, Paul H.},
  title = {First Order and Second Order Phase Transitions in Gauge Theories at Finite Temperature},
  journal = {Nuclear Physics B}, volume = {170}, pages = {388--408},
  year = {1980}, doi = {10.1016/0550-3213(80)90418-6}
}

@article{Linde1980,
  author = {Linde, A. D.},
  title = {Infrared problem in the thermodynamics of the {Yang--Mills} gas},
  journal = {Physics Letters B}, volume = {96}, number = {3--4},
  pages = {289--292}, year = {1980}, doi = {10.1016/0370-2693(80)90769-8}
}

@article{Feynman1981,
  author = {Feynman, Richard P.},
  title = {The qualitative behavior of {Yang--Mills} theory in {2+1} dimensions},
  journal = {Nuclear Physics B}, volume = {188}, number = {3},
  pages = {479--512}, year = {1981}, doi = {10.1016/0550-3213(81)90005-5}
}

@article{JackiwTempleton1981,
  author = {Jackiw, R. and Templeton, S.},
  title = {How super-renormalizable interactions cure their infrared divergences},
  journal = {Physical Review D}, volume = {23}, number = {10},
  pages = {2291--2304}, year = {1981}, doi = {10.1103/PhysRevD.23.2291}
}

@article{AppelquistPisarski1981,
  author = {Appelquist, Thomas and Pisarski, Robert D.},
  title = {High-temperature {Yang--Mills} theories and three-dimensional quantum chromodynamics},
  journal = {Physical Review D}, volume = {23}, number = {10},
  pages = {2305--2317}, year = {1981}, doi = {10.1103/PhysRevD.23.2305}
}

@article{Hooft1979,
  author = {{'t Hooft}, Gerard},
  title = {A property of electric and magnetic flux in non-Abelian gauge theories},
  journal = {Nuclear Physics B}, volume = {153}, pages = {141--160},
  year = {1979}, doi = {10.1016/0550-3213(79)90595-9}
}

@incollection{GonzalezArroyo1983,
  author = {Gonz{\'a}lez-Arroyo, Antonio and Jurkiewicz, J. and Korthals-Altes, C. P.},
  title = {Ground State Metamorphosis for {Yang--Mills} Fields on a Finite Periodic Lattice},
  booktitle = {Structural Elements in Particle Physics and Statistical Mechanics},
  editor = {Honerkamp, J. and Pohlmeyer, K. and R{\"o}mer, H.},
  publisher = {Plenum Press}, address = {New York}, pages = {339--358},
  year = {1983}, doi = {10.1007/978-1-4613-3509-2_25},
  note = {Freiburg 1981 lectures. Year follows the publisher's original-volume record (1983); the chapter landing page inconsistently displays 1987.}
}

@article{LuscherMunster1984,
  author = {L{\"u}scher, Martin and M{\"u}nster, Gernot},
  title = {Weak-coupling expansion of the low-lying energy values in the {SU(2)} gauge theory on a torus},
  journal = {Nuclear Physics B}, volume = {232}, number = {3},
  pages = {445--472}, year = {1984}, doi = {10.1016/0550-3213(84)90038-5}
}

@article{KollerVanBaal1988,
  author = {Koller, Jeffrey and van Baal, Pierre},
  title = {A non-perturbative analysis in finite volume gauge theory},
  journal = {Nuclear Physics B}, volume = {302}, number = {1},
  pages = {1--64}, year = {1988}, doi = {10.1016/0550-3213(88)90665-7}
}

@incollection{VanBaal2001,
  author = {van Baal, Pierre}, title = {{QCD} in a Finite Volume},
  booktitle = {At the Frontier of Particle Physics: Handbook of {QCD}},
  editor = {Shifman, M.}, volume = {2}, publisher = {World Scientific},
  pages = {683--760}, year = {2001}, doi = {10.1142/9789812810458_0021},
  eprint = {hep-ph/0008206}, archivePrefix = {arXiv}
}

@misc{GonzalezArroyo1998,
  author = {Gonz{\'a}lez-Arroyo, Antonio},
  title = {{Yang--Mills} Fields on the 4-dimensional torus. Part {I}: Classical Theory},
  year = {1998}, eprint = {hep-th/9807108}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/hep-th/9807108},
  note = {First part of lectures given at the 1997 Advanced School on Non-perturbative Quantum Physics, Pe{\~n}iscola; cited version: arXiv:hep-th/9807108v1.}
}

@article{Karabali1998a,
  author = {Karabali, Dimitra and Kim, Chanju and Nair, V. P.},
  title = {Planar {Yang--Mills} theory: {Hamiltonian}, regulators and mass gap},
  journal = {Nuclear Physics B}, volume = {524}, pages = {661--694},
  year = {1998}, doi = {10.1016/S0550-3213(98)00309-5},
  eprint = {hep-th/9705087}, archivePrefix = {arXiv}
}

@article{Karabali1998b,
  author = {Karabali, Dimitra and Kim, Chanju and Nair, V. P.},
  title = {On the vacuum wavefunction and string tension of {Yang--Mills} theories in {(2+1)} dimensions},
  journal = {Physics Letters B}, volume = {434}, number = {1--2},
  pages = {103--109}, year = {1998}, doi = {10.1016/S0370-2693(98)00751-5},
  eprint = {hep-th/9804132}, archivePrefix = {arXiv}
}

@article{Teper1999,
  author = {Teper, Michael J.}, title = {{SU(N)} gauge theories in {2+1} dimensions},
  journal = {Physical Review D}, volume = {59}, number = {1},
  pages = {014512}, year = {1999}, doi = {10.1103/PhysRevD.59.014512},
  eprint = {hep-lat/9804008}, archivePrefix = {arXiv},
  note = {Issue dated 1 January 1999; first published online 9 December 1998}
}

@incollection{Brydges1986,
  author = {Brydges, David C.},
  title = {A short course on cluster expansions},
  editor = {Osterwalder, Konrad and Stora, Raymond},
  booktitle = {Critical Phenomena, Random Systems, Gauge Theories, Part I},
  series = {Les Houches, Session XLIII, 1984},
  publisher = {North-Holland}, address = {Amsterdam},
  pages = {129--183}, year = {1986},
  url = {https://inspirehep.net/literature/211093},
  note = {School held in 1984; proceedings published in 1986. No DOI or arXiv identifier found}
}

@article{Prokhorov1956,
  author = {Prokhorov, Yu. V.},
  title = {Convergence of random processes and limit theorems in probability theory},
  journal = {Theory of Probability and Its Applications},
  volume = {1}, number = {2}, pages = {157--214}, year = {1956},
  doi = {10.1137/1101016},
  url = {https://epubs.siam.org/doi/10.1137/1101016},
  note = {English translation; Russian original: Teoriya Veroyatnostei i ee Primeneniya 1(2), 177--238 (1956)}
}

@incollection{Penrose1967,
  author = {Penrose, Oliver},
  title = {Convergence of fugacity expansions for classical systems},
  editor = {Bak, Thor A.},
  booktitle = {Statistical Mechanics: Foundations and Applications},
  pages = {101--109},
  publisher = {W. A. Benjamin},
  address = {New York},
  year = {1967},
}

@book{Billingsley1999,
  author = {Billingsley, Patrick},
  title = {Convergence of Probability Measures},
  edition = {Second},
  series = {Wiley Series in Probability and Statistics},
  publisher = {John Wiley \& Sons, New York},
  year = {1999},
  doi = {10.1002/9780470316962},
}

@article{EckartYoung1936,
  author = {Eckart, Carl and Young, Gale},
  title = {The approximation of one matrix by another of lower rank},
  journal = {Psychometrika},
  volume = {1},
  number = {3},
  pages = {211--218},
  year = {1936},
  doi = {10.1007/BF02288367},
}

@article{AldousEagleson1978,
  author = {Aldous, David J. and Eagleson, Geoffrey K.},
  title = {On mixing and stability of limit theorems},
  journal = {Annals of Probability},
  volume = {6},
  number = {2},
  pages = {325--331},
  year = {1978},
  doi = {10.1214/aop/1176995577},
}

@article{Chatterjee2026HiggsScaling,
  author = {Chatterjee, Sourav},
  title = {A Scaling Limit of {SU(2)} Lattice {Yang--Mills--Higgs} Theory},
  journal = {Probability and Mathematical Physics},
  volume = {7},
  number = {2},
  pages = {339--381},
  year = {2026},
  doi = {10.2140/pmp.2026.7.339},
  eprint = {2401.10507v4},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2401.10507v4},
}

@misc{ChevyrevQuShen2026,
  author = {Chevyrev, Ilya and Qu, Yahui and Shen, Hao},
  title = {Scaling Limit of the {3D} Abelian {Yang--Mills} Langevin Dynamics},
  year = {2026},
  eprint = {2608.27828v2},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/2608.27828v2},
  note = {Preprint, version 2, 17 September 2026},
}