%
%

@article{Po77,
  author  = {Polyakov, A. M.},
  title   = {Quark confinement and topology of gauge theories},
  journal = {Nuclear Phys. B},
  volume  = {120},
  year    = {1977},
  pages   = {429--458},
  doi     = {10.1016/0550-3213(77)90086-4}
}

@article{BMK77,
  author  = {Banks, T. and Myerson, R. and Kogut, J.},
  title   = {Phase transitions in {A}belian lattice gauge theories},
  journal = {Nuclear Phys. B},
  volume  = {129},
  year    = {1977},
  pages   = {493--510},
  doi     = {10.1016/0550-3213(77)90129-8}
}

@article{GM82,
  author  = {G{\"o}pfert, M. and Mack, G.},
  title   = {Proof of confinement of static quarks in 3-dimensional {U}(1) lattice gauge theory for all values of the coupling constant},
  journal = {Comm. Math. Phys.},
  volume  = {82},
  year    = {1982},
  pages   = {545--606},
  doi     = {10.1007/BF01961240},
  note    = {Preprint DESY 81-036 (1981); equation, section and page numbers cited in this paper refer to the preprint}
}

@techreport{GM82pre,
  author      = {G{\"o}pfert, M. and Mack, G.},
  title       = {Proof of confinement of static quarks in 3-dimensional {U}(1) lattice gauge theory for all values of the coupling constant},
  institution = {DESY},
  type        = {Preprint},
  number      = {DESY 81-036},
  year        = {1981},
  note        = {Preprint version of \cite{GM82}}
}

@article{GM81,
  author  = {G{\"o}pfert, M. and Mack, G.},
  title   = {Iterated {M}ayer expansion for classical gases at low temperatures},
  journal = {Comm. Math. Phys.},
  volume  = {81},
  year    = {1981},
  pages   = {97--126},
  doi     = {10.1007/BF01941802},
  note    = {Preprint DESY 81-014 (1981); equation, section and page numbers cited in this paper refer to the preprint}
}

@techreport{GM81pre,
  author      = {G{\"o}pfert, M. and Mack, G.},
  title       = {Iterated {M}ayer expansion for classical gases at low temperatures},
  institution = {DESY},
  type        = {Preprint},
  number      = {DESY 81-014},
  year        = {1981},
  note        = {Preprint version of \cite{GM81}}
}

@article{BF80,
  author  = {Brydges, D. C. and Federbush, P.},
  title   = {Debye screening},
  journal = {Comm. Math. Phys.},
  volume  = {73},
  year    = {1980},
  pages   = {197--246},
  doi     = {10.1007/BF01197700}
}

@article{B78,
  author  = {Brydges, D. C.},
  title   = {A rigorous approach to {D}ebye screening in dilute classical {C}oulomb systems},
  journal = {Comm. Math. Phys.},
  volume  = {58},
  year    = {1978},
  pages   = {313--350},
  doi     = {10.1007/BF01614227}
}

@article{BF76,
  author  = {Brydges, D. and Federbush, P.},
  title   = {The cluster expansion in statistical mechanics},
  journal = {Comm. Math. Phys.},
  volume  = {49},
  year    = {1976},
  pages   = {233--246},
  doi     = {10.1007/BF01608729}
}

@article{BF77,
  author  = {Brydges, D. and Federbush, P.},
  title   = {The cluster expansion for potentials with exponential fall-off},
  journal = {Comm. Math. Phys.},
  volume  = {53},
  year    = {1977},
  pages   = {19--30},
  doi     = {10.1007/BF01609165}
}

@misc{TomLean,
  author = {Tejasvi Singh Tomar},
  title = {A {Lean}~4 formalization of the area law for three-dimensional {$U(1)$} lattice gauge theory with the {Wilson} action},
  year = {2026},
  note = {Zenodo, \url{https://doi.org/10.5281/zenodo.23480809}}
}

@article{BK87,
  author = {D. C. Brydges and T. Kennedy},
  title = {Mayer expansions and the {H}amilton--{J}acobi equation},
  journal = {J. Stat. Phys.},
  volume = {48},
  year = {1987},
  pages = {19--49}
}

@incollection{AR95,
  author = {A. Abdesselam and V. Rivasseau},
  title = {Trees, forests and jungles: a botanical garden for cluster expansions},
  booktitle = {Constructive Physics},
  series = {Lecture Notes in Physics},
  volume = {446},
  publisher = {Springer},
  address = {Berlin},
  year = {1995},
  pages = {7--36}
}

@book{SW71,
  author = {E. M. Stein and G. Weiss},
  title = {Introduction to Fourier Analysis on {E}uclidean Spaces},
  series = {Princeton Mathematical Series},
  volume = {32},
  publisher = {Princeton University Press},
  address = {Princeton},
  year = {1971}
}

@article{Gi70,
  author  = {Ginibre, J.},
  title   = {General formulation of {G}riffiths' inequalities},
  journal = {Comm. Math. Phys.},
  volume  = {16},
  year    = {1970},
  pages   = {310--328},
  doi     = {10.1007/BF01646537}
}

@article{Gu80,
  author  = {Guth, A. H.},
  title   = {Existence proof of a nonconfining phase in four-dimensional {U}(1) lattice gauge theory},
  journal = {Phys. Rev. D},
  volume  = {21},
  year    = {1980},
  pages   = {2291--2307},
  doi     = {10.1103/PhysRevD.21.2291},
  note    = {Preprint CLNS 79/439 (1979); lemma numbers cited in this paper are those of the preprint}
}

@article{Fr79,
  author  = {Fr{\"o}hlich, J.},
  title   = {Confinement in {$Z_n$} lattice gauge theories implies confinement in {SU}(n) lattice {H}iggs theories},
  journal = {Phys. Lett. B},
  volume  = {83},
  year    = {1979},
  pages   = {195--198},
  doi     = {10.1016/0370-2693(79)90684-1},
  note    = {Preprint IHES/P/79/02; equation numbers cited in this paper are those of the preprint}
}

@article{MMSP78,
  author  = {Messager, A. and Miracle-Sol{\'e}, S. and Pfister, C.},
  title   = {Correlation inequalities and uniqueness of the equilibrium state for the plane rotator ferromagnetic model},
  journal = {Comm. Math. Phys.},
  volume  = {58},
  year    = {1978},
  pages   = {19--29},
  doi     = {10.1007/BF01624786}
}

@article{OS78,
  author  = {Osterwalder, K. and Seiler, E.},
  title   = {Gauge field theories on a lattice},
  journal = {Ann. Physics},
  volume  = {110},
  year    = {1978},
  pages   = {440--471},
  doi     = {10.1016/0003-4916(78)90039-8}
}

@article{GJ77,
  author  = {Glimm, J. and Jaffe, A.},
  title   = {Quark trapping for lattice {U}(1) gauge fields},
  journal = {Phys. Lett. B},
  volume  = {66},
  year    = {1977},
  pages   = {67--69},
  doi     = {10.1016/0370-2693(77)90615-3}
}

@misc{Ch26,
  author  = {Chatterjee, S.},
  title   = {A short proof of confinement in three-dimensional lattice gauge theories with a central {U}(1)},
  year    = {2026},
  note    = {arXiv:2602.00436, version 2 (June 2026); to appear in Adv. Nonlinear Stud.}
}

@article{FS81,
  author  = {Fr{\"o}hlich, J. and Spencer, T.},
  title   = {On the statistical mechanics of classical {C}oulomb and dipole gases},
  journal = {J. Statist. Phys.},
  volume  = {24},
  year    = {1981},
  pages   = {617--701},
  doi     = {10.1007/BF01011379}
}

@article{FS82,
  author  = {Fr{\"o}hlich, J. and Spencer, T.},
  title   = {Massless phases and symmetry restoration in {A}belian gauge theories and spin systems},
  journal = {Comm. Math. Phys.},
  volume  = {83},
  year    = {1982},
  pages   = {411--454},
  doi     = {10.1007/BF01213610}
}

@incollection{FPS82,
  author    = {Fr{\"o}hlich, J. and Pfister, C.-E. and Spencer, T.},
  title     = {On the statistical mechanics of surfaces},
  booktitle = {Stochastic Processes in Quantum Theory and Statistical Physics},
  series    = {Lecture Notes in Phys.},
  volume    = {173},
  publisher = {Springer},
  address   = {Berlin},
  year      = {1982},
  pages     = {169--199},
  doi       = {10.1007/3-540-11956-6_118}
}

@article{Ki86,
  author  = {King, C.},
  title   = {Deconfining phase transition in the {U}(1) model with {W}ilson's action},
  journal = {Comm. Math. Phys.},
  volume  = {105},
  year    = {1986},
  pages   = {675--690},
  doi     = {10.1007/BF01238939}
}

@article{Gr83,
  author  = {Gross, L.},
  title   = {Convergence of {${\rm U}(1)_3$} lattice gauge theory to its continuum limit},
  journal = {Comm. Math. Phys.},
  volume  = {92},
  year    = {1983},
  pages   = {137--162},
  doi     = {10.1007/BF01210842}
}

@article{HW74,
  author  = {Hartman, P. and Watson, G. S.},
  title   = {``{N}ormal'' distribution functions on spheres and the modified {B}essel functions},
  journal = {Ann. Probability},
  volume  = {2},
  year    = {1974},
  pages   = {593--607},
  doi     = {10.1214/aop/1176996606}
}

@article{Yo80,
  author  = {Yor, M.},
  title   = {Loi de l'indice du lacet brownien, et distribution de {H}artman\textendash {W}atson},
  journal = {Z. Wahrsch. Verw. Gebiete},
  volume  = {53},
  year    = {1980},
  pages   = {71--95},
  doi     = {10.1007/BF00531612}
}

@article{LSS97,
  author  = {Liggett, T. M. and Schonmann, R. H. and Stacey, A. M.},
  title   = {Domination by product measures},
  journal = {Ann. Probab.},
  volume  = {25},
  year    = {1997},
  pages   = {71--95},
  doi     = {10.1214/aop/1024404279}
}

@article{Am74,
  author  = {Amos, D. E.},
  title   = {Computation of modified {B}essel functions and their ratios},
  journal = {Math. Comp.},
  volume  = {28},
  year    = {1974},
  pages   = {239--251},
  doi     = {10.2307/2005830}
}

@article{TN51,
  author  = {Thiruvenkatachar, V. R. and Nanjundiah, T. S.},
  title   = {Inequalities concerning {B}essel functions and orthogonal polynomials},
  journal = {Proc. Indian Acad. Sci. Sect. A},
  volume  = {33},
  year    = {1951},
  pages   = {373--384},
  doi     = {10.1007/BF03178130}
}

@misc{AHPS,
  author  = {Aizenman, M. and Harel, M. and Peled, R. and Shapiro, J.},
  title   = {Depinning in integer-restricted {G}aussian fields and {BKT} phases of two-component spin models},
  year    = {2021},
  note    = {arXiv:2110.09498}
}

@misc{OAI216,
  author  = {{OpenAI}},
  title   = {The critical correlation exponent of the planar {XY} model},
  year    = {2026},
  note    = {Manuscript dated September~24, 2026, family~216 of the repository \url{https://github.com/openai/math}}
}

@misc{DvEG,
  author  = {Dario, P. and van Engelenburg, D. and Garban, C.},
  title   = {The impact of disorder and non-convex interactions on delocalisation of height functions},
  year    = {2026},
  note    = {arXiv:2604.24743}
}

@article{CG25,
  author  = {Chevyrev, I. and Garban, C.},
  title   = {Villain action in lattice gauge theory},
  journal = {J. Stat. Phys.},
  volume  = {192},
  year    = {2025},
  pages   = {38},
  doi     = {10.1007/s10955-025-03420-1}
}

@article{CPS25,
  author  = {Cao, S. and Park, M. and Sheffield, S.},
  title   = {Random surfaces and lattice {Y}ang\textendash {M}ills},
  journal = {Commun. Amer. Math. Soc.},
  volume  = {5},
  year    = {2025},
  pages   = {774--896},
  doi     = {10.1090/cams/59}
}

@misc{CNS,
  author  = {Cao, S. and Nissim, R. and Sheffield, S.},
  title   = {Expanded regimes of area law for lattice {Y}ang\textendash {M}ills theories},
  year    = {2025},
  note    = {arXiv:2505.16585}
}

@misc{Fo,
  author  = {Forsstr{\"o}m, M. P.},
  title   = {Phase transitions in the charged compact {A}belian lattice {H}iggs model},
  year    = {2026},
  note    = {arXiv:2602.21679}
}

@misc{Ni,
  author  = {Nissim, R.},
  title   = {{U}({N}) lattice {Y}ang\textendash {M}ills in the 't {H}ooft regime},
  year    = {2025},
  note    = {arXiv:2510.22788}
}

@misc{AGP26,
  author  = {Adhikari, A. and Gheissari, R. and Peled, R.},
  title   = {On the rigidity of sloped height functions in $d\ge3$ and non-crossing surfaces},
  year    = {2026},
  note    = {arXiv:2609.01499}
}

@article{Ti,
  author  = {Tim{\'a}r, {\'A}.},
  title   = {Boundary-connectivity via graph theory},
  journal = {Proc. Amer. Math. Soc.},
  volume  = {141},
  year    = {2013},
  pages   = {475--480},
  doi     = {10.1090/S0002-9939-2012-11333-4}
}

@article{Ke87,
  author  = {Kesten, H.},
  title   = {Surfaces with minimal random weights and maximal flows: a higher dimensional version of first-passage percolation},
  journal = {Illinois J. Math.},
  volume  = {31},
  year    = {1987},
  pages   = {99--166},
  doi     = {10.1215/ijm/1255989405}
}

@article{BL91,
  author  = {Bollob{\'a}s, B. and Leader, I.},
  title   = {Edge-isoperimetric inequalities in the grid},
  journal = {Combinatorica},
  volume  = {11},
  year    = {1991},
  pages   = {299--314},
  doi     = {10.1007/BF01275667}
}

@article{Ba04,
  author  = {Barlow, M. T.},
  title   = {Random walks on supercritical percolation clusters},
  journal = {Ann. Probab.},
  volume  = {32},
  year    = {2004},
  pages   = {3024--3084},
  doi     = {10.1214/009117904000000748}
}

@book{LL10,
  author    = {Lawler, G. F. and Limic, V.},
  title     = {Random Walk: A Modern Introduction},
  series    = {Cambridge Stud. Adv. Math.},
  volume    = {123},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  year      = {2010}
}

@article{LW49,
  author  = {Loomis, L. H. and Whitney, H.},
  title   = {An inequality related to the isoperimetric inequality},
  journal = {Bull. Amer. Math. Soc.},
  volume  = {55},
  year    = {1949},
  pages   = {961--962},
  doi     = {10.1090/S0002-9904-1949-09320-5}
}

%

@article{CT73,
  author  = {Combes, J. M. and Thomas, L.},
  title   = {Asymptotic behaviour of eigenfunctions for multiparticle {S}chr{\"o}dinger operators},
  journal = {Comm. Math. Phys.},
  volume  = {34},
  year    = {1973},
  pages   = {251--270},
  doi     = {10.1007/BF01646473}
}

@article{GK04,
  author  = {Galvin, D. and Kahn, J.},
  title   = {On phase transition in the hard-core model on {$\mathbb{Z}^d$}},
  journal = {Combin. Probab. Comput.},
  volume  = {13},
  year    = {2004},
  pages   = {137--164},
  doi     = {10.1017/S0963548303006035}
}

@article{Wat39,
  author  = {Watson, G. N.},
  title   = {Three triple integrals},
  journal = {Quart. J. Math. Oxford Ser.},
  volume  = {10},
  year    = {1939},
  pages   = {266--276},
  doi     = {10.1093/qmath/os-10.1.266}
}

@article{GZ77,
  author  = {Glasser, M. L. and Zucker, I. J.},
  title   = {Extended {W}atson integrals for the cubic lattices},
  journal = {Proc. Nat. Acad. Sci. U.S.A.},
  volume  = {74},
  year    = {1977},
  pages   = {1800--1801},
  doi     = {10.1073/pnas.74.5.1800}
}

@article{Zu11,
  author  = {Zucker, I. J.},
  title   = {70+ years of the {W}atson integrals},
  journal = {J. Stat. Phys.},
  volume  = {145},
  year    = {2011},
  pages   = {591--612},
  doi     = {10.1007/s10955-011-0273-0}
}

@article{FS81KT,
  author  = {Fr{\"o}hlich, J. and Spencer, T.},
  title   = {The {K}osterlitz\textendash {T}houless transition in two-dimensional {A}belian spin systems and the {C}oulomb gas},
  journal = {Comm. Math. Phys.},
  volume  = {81},
  year    = {1981},
  pages   = {527--602},
  doi     = {10.1007/BF01208273},
  note    = {Preprint IHES/P/81/25; section numbers cited in this paper are those of the preprint}
}

@article{DG25,
  author  = {Dario, P. and Garban, C.},
  title   = {Phase transitions for the {XY} model in non-uniformly elliptic and {P}oisson\textendash {V}oronoi environments},
  journal = {Comm. Math. Phys.},
  volume  = {406},
  year    = {2025},
  pages   = {101},
  doi     = {10.1007/s00220-025-05269-7}
}

@article{GS23,
  author  = {Garban, C. and Sep{\'u}lveda, A.},
  title   = {Improved spin-wave estimate for {W}ilson loops in {U}(1) lattice gauge theory},
  journal = {Int. Math. Res. Not. IMRN},
  volume  = {2023},
  number  = {21},
  year    = {2023},
  pages   = {18142--18198},
  doi     = {10.1093/imrn/rnac356},
  note    = {arXiv:2107.04021}
}

@book{LP16,
  author    = {Lyons, R. and Peres, Y.},
  title     = {Probability on Trees and Networks},
  publisher = {Cambridge University Press},
  address   = {New York},
  year      = {2016},
  doi       = {10.1017/9781316672815}
}

@article{Har76,
  author  = {Hartman, P.},
  title   = {Completely monotone families of solutions of $n$-th order linear differential equations and infinitely divisible distributions},
  journal = {Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)},
  volume  = {3},
  year    = {1976},
  pages   = {267--287}
}

@article{Pat09,
  author  = {Patie, P.},
  title   = {Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of {L}{\'e}vy processes},
  journal = {Ann. Inst. Henri Poincar{\'e} Probab. Stat.},
  volume  = {45},
  year    = {2009},
  pages   = {667--684},
  doi     = {10.1214/08-AIHP182}
}

@article{CE43,
  author  = {Clarkson, J. A. and Erd{\H{o}}s, P.},
  title   = {Approximation by polynomials},
  journal = {Duke Math. J.},
  volume  = {10},
  year    = {1943},
  pages   = {5--11},
  doi     = {10.1215/S0012-7094-43-01002-6}
}

@article{Alm07,
  author  = {Almira, J. M.},
  title   = {M{\"u}ntz type theorems. {I}},
  journal = {Surv. Approx. Theory},
  volume  = {3},
  year    = {2007},
  pages   = {152--194},
  note    = {arXiv:0710.3570}
}