@article{ck1993,
  author = {Cugliandolo, Leticia F. and Kurchan, Jorge},
  title = {Analytical solution of the off-equilibrium dynamics
           of a long-range spin-glass model},
  journal = {Physical Review Letters},
  volume = {71}, number = {1}, pages = {173--176}, year = {1993},
  doi = {10.1103/PhysRevLett.71.173},
  eprint = {cond-mat/9303036}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/cond-mat/9303036}
}

@article{cs1992,
  author = {Crisanti, Andrea and Sommers, Hans-J{\"u}rgen},
  title = {The spherical {$p$}-spin interaction spin glass model:
           the statics},
  journal = {Zeitschrift f{\"u}r Physik B Condensed Matter},
  volume = {87}, number = {3}, pages = {341--354}, year = {1992},
  doi = {10.1007/BF01309287},
  url = {https://link.springer.com/article/10.1007/BF01309287}
}

@article{chs1993,
  author = {Crisanti, Andrea and Horner, Heinz
            and Sommers, Hans-J{\"u}rgen},
  title = {The spherical {$p$}-spin interaction spin-glass model:
           the dynamics},
  journal = {Zeitschrift f{\"u}r Physik B Condensed Matter},
  volume = {92}, number = {2}, pages = {257--271}, year = {1993},
  doi = {10.1007/BF01312184},
  url = {https://link.springer.com/article/10.1007/BF01312184}
}

@article{bag2001,
  author = {Ben Arous, G{\'e}rard and Dembo, Amir and Guionnet, Alice},
  title = {Aging of spherical spin glasses},
  journal = {Probability Theory and Related Fields},
  volume = {120}, number = {1}, pages = {1--67}, year = {2001},
  doi = {10.1007/PL00008774},
  url = {https://link.springer.com/article/10.1007/PL00008774}
}

@article{bag2006,
  author = {Ben Arous, G{\'e}rard and Dembo, Amir and Guionnet, Alice},
  title = {{Cugliandolo--Kurchan} equations for dynamics of spin-glasses},
  journal = {Probability Theory and Related Fields},
  volume = {136}, number = {4}, pages = {619--660}, year = {2006},
  doi = {10.1007/s00440-005-0491-y},
  eprint = {math/0409273}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math/0409273}
}

@article{dgm2007,
  author = {Dembo, Amir and Guionnet, Alice and Mazza, Christian},
  title = {Limiting dynamics for spherical models of spin glasses
           at high temperature},
  journal = {Journal of Statistical Physics},
  volume = {128}, number = {4}, pages = {847--881}, year = {2007},
  doi = {10.1007/s10955-006-9239-z},
  eprint = {math/0609546}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math/0609546}
}

@article{guionnetmazza2005,
  author = {Guionnet, Alice and Mazza, Christian},
  title = {Long time behaviour of the solution to non-linear
           {Kraichnan} equations},
  journal = {Probability Theory and Related Fields},
  volume = {131}, number = {4}, pages = {493--518}, year = {2005},
  doi = {10.1007/s00440-004-0382-7},
  eprint = {math/0409274}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math/0409274}
}

@article{ds2020,
  author = {Dembo, Amir and Subag, Eliran},
  title = {Dynamics for spherical spin glasses:
           disorder dependent initial conditions},
  journal = {Journal of Statistical Physics},
  volume = {181}, number = {2}, pages = {465--514}, year = {2020},
  doi = {10.1007/s10955-020-02587-z},
  eprint = {1908.01126}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1908.01126}
}

@misc{ds2025,
  author = {Dembo, Amir and Subag, Eliran},
  title = {Dynamics for spherical spin glasses:
           {Gibbs} distributed initial conditions},
  year = {2025},
  doi = {10.48550/arXiv.2503.23342},
  eprint = {2503.23342}, archivePrefix = {arXiv},
  primaryClass = {math.PR},
  note = {arXiv version 3, 8 July 2026},
  url = {https://arxiv.org/abs/2503.23342}
}

@article{sellke2024,
  author = {Sellke, Mark},
  title = {The threshold energy of low temperature {Langevin}
           dynamics for pure spherical spin glasses},
  journal = {Communications on Pure and Applied Mathematics},
  volume = {77}, number = {11}, pages = {4065--4099}, year = {2024},
  doi = {10.1002/cpa.22197},
  eprint = {2305.07956}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2305.07956}
}

@misc{hs2023,
  author = {Huang, Brice and Sellke, Mark},
  title = {Algorithmic threshold for multi-species spherical spin glasses},
  year = {2023},
  doi = {10.48550/arXiv.2303.12172},
  eprint = {2303.12172}, archivePrefix = {arXiv},
  primaryClass = {math.PR},
  note = {arXiv version 2, 13 September 2023},
  url = {https://arxiv.org/abs/2303.12172}
}

@article{hs2021,
  author = {Huang, Brice and Sellke, Mark},
  title = {Tight {Lipschitz} hardness for optimizing mean field spin glasses},
  journal = {Communications on Pure and Applied Mathematics},
  volume = {78}, number = {1}, pages = {60--119}, year = {2025},
  doi = {10.1002/cpa.22222},
  eprint = {2110.07847}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2110.07847}
}

@article{abc2013,
  author = {Auffinger, Antonio and Ben Arous, G{\'e}rard
            and {\v{C}}ern{\'y}, Ji{\v{r}}{\'i}},
  title = {Random matrices and complexity of spin glasses},
  journal = {Communications on Pure and Applied Mathematics},
  volume = {66}, number = {2}, pages = {165--201}, year = {2013},
  doi = {10.1002/cpa.21422},
  eprint = {1003.1129}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1003.1129}
}

@article{cdk1997,
  author = {Cugliandolo, Leticia F. and Dean, David S. and Kurchan, Jorge},
  title = {Fluctuation-dissipation theorems and entropy production
           in relaxational systems},
  journal = {Physical Review Letters},
  volume = {79}, number = {12}, pages = {2168--2171}, year = {1997},
  doi = {10.1103/PhysRevLett.79.2168},
  eprint = {cond-mat/9705002}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/cond-mat/9705002}
}

@article{bbm1996,
  author = {Barrat, Alain and Burioni, Raffaella and M{\'e}zard, Marc},
  title = {Ageing classification in glassy dynamics},
  journal = {Journal of Physics A: Mathematical and General},
  volume = {29}, number = {7}, pages = {1311--1330}, year = {1996},
  doi = {10.1088/0305-4470/29/7/005},
  eprint = {cond-mat/9509142}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/cond-mat/9509142}
}

@article{franzvirasoro2000,
  author = {Franz, Silvio and Virasoro, Miguel A.},
  title = {Quasi-equilibrium interpretation of ageing dynamics},
  journal = {Journal of Physics A: Mathematical and General},
  volume = {33}, number = {5}, pages = {891--905}, year = {2000},
  doi = {10.1088/0305-4470/33/5/306},
  eprint = {cond-mat/9907438}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/cond-mat/9907438}
}

@article{biroli1999,
  author = {Biroli, Giulio},
  title = {Dynamical {TAP} approach to mean field glassy systems},
  journal = {Journal of Physics A: Mathematical and General},
  volume = {32}, number = {48}, pages = {8365--8388}, year = {1999},
  doi = {10.1088/0305-4470/32/48/301},
  eprint = {cond-mat/9909415}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/cond-mat/9909415}
}

@article{fv2002,
  author = {Franosch, Thomas and Voigtmann, Thomas},
  title = {Completely monotone solutions of the mode-coupling theory
           for mixtures},
  journal = {Journal of Statistical Physics},
  volume = {109}, number = {1--2}, pages = {237--259}, year = {2002},
  doi = {10.1023/A:1019991729106},
  eprint = {cond-mat/0202238}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/cond-mat/0202238}
}

@article{gs1995,
  author = {G{\"o}tze, Wolfgang and Sj{\"o}gren, Lennart},
  title = {General properties of certain non-linear
           integro-differential equations},
  journal = {Journal of Mathematical Analysis and Applications},
  volume = {195}, number = {1}, pages = {230--250}, year = {1995},
  doi = {10.1006/jmaa.1995.1352},
  url = {https://doi.org/10.1006/jmaa.1995.1352}
}

@article{sjogren2003,
  author = {Sj{\"o}gren, Lennart},
  title = {Regenerative processes in supercooled liquids and glasses},
  journal = {Physica A: Statistical Mechanics and its Applications},
  volume = {322}, pages = {81--117}, year = {2003},
  doi = {10.1016/S0378-4371(02)01832-0},
  url = {https://www.sciencedirect.com/science/article/abs/pii/S0378437102018320}
}

@article{goetzesjogren1992,
  author = {G{\"o}tze, Wolfgang and Sj{\"o}gren, Lennart},
  title = {Relaxation processes in supercooled liquids},
  journal = {Reports on Progress in Physics},
  volume = {55}, number = {3}, pages = {241--376}, year = {1992},
  doi = {10.1088/0034-4885/55/3/001},
  url = {https://doi.org/10.1088/0034-4885/55/3/001}
}

@book{goetze2009,
  author = {G{\"o}tze, Wolfgang},
  title = {Complex Dynamics of Glass-Forming Liquids:
           A Mode-Coupling Theory},
  publisher = {Oxford University Press},
  year = {2009},
  series = {International Series of Monographs on Physics},
  volume = {143},
  doi = {10.1093/acprof:oso/9780199235346.001.0001},
  url = {https://academic.oup.com/book/10864}
}

@book{bgt1987,
  author = {Bingham, Nicholas H. and Goldie, Charles M.
            and Teugels, Jozef L.},
  title = {Regular Variation},
  publisher = {Cambridge University Press},
  year = {1987},
  series = {Encyclopedia of Mathematics and its Applications},
  volume = {27},
  doi = {10.1017/CBO9780511721434},
  url = {https://doi.org/10.1017/CBO9780511721434}
}

@book{bgl2014,
  author = {Bakry, Dominique and Gentil, Ivan and Ledoux, Michel},
  title = {Analysis and Geometry of {Markov} Diffusion Operators},
  publisher = {Springer},
  year = {2014},
  series = {Grundlehren der mathematischen Wissenschaften},
  volume = {348},
  doi = {10.1007/978-3-319-00227-9},
  url = {https://link.springer.com/book/10.1007/978-3-319-00227-9}
}

@book{janson1997,
  author = {Janson, Svante},
  title = {Gaussian Hilbert Spaces},
  publisher = {Cambridge University Press},
  year = {1997},
  series = {Cambridge Tracts in Mathematics},
  volume = {129},
  doi = {10.1017/CBO9780511526169},
  url = {https://doi.org/10.1017/CBO9780511526169}
}

@article{shattering2025,
  author = {El Alaoui, Ahmed and Montanari, Andrea and Sellke, Mark},
  title = {Shattering in pure spherical spin glasses},
  journal = {Communications in Mathematical Physics},
  volume = {406}, number = {5},
  pages = {111}, eid = {111}, year = {2025},
  doi = {10.1007/s00220-025-05243-3},
  eprint = {2307.04659}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2307.04659}
}

@article{sellke2025,
  author = {Sellke, Mark},
  title = {On marginal stability in low temperature spherical spin glasses},
  journal = {Communications in Mathematical Physics},
  volume = {406}, number = {9},
  pages = {227}, eid = {227}, year = {2025},
  doi = {10.1007/s00220-025-05410-6},
  eprint = {2409.15728}, archivePrefix = {arXiv},
  note = {arXiv version 4, 23 August 2026},
  url = {https://arxiv.org/abs/2409.15728}
}

@book{widder1941,
  author = {Widder, David Vernon},
  title = {The Laplace Transform},
  publisher = {Princeton University Press},
  year = {1941},
  series = {Princeton Mathematical Series},
  volume = {6},
  url = {https://www.jstor.org/stable/j.ctt183ptft}
}

@book{bcr1984,
  author = {Berg, Christian and Christensen, Jens Peter Reus
            and Ressel, Paul},
  title = {Harmonic Analysis on Semigroups:
           Theory of Positive Definite and Related Functions},
  publisher = {Springer},
  year = {1984},
  series = {Graduate Texts in Mathematics},
  volume = {100},
  doi = {10.1007/978-1-4612-1128-0},
  url = {https://link.springer.com/book/10.1007/978-1-4612-1128-0}
}

@book{feller1971,
  author = {Feller, William},
  title = {An Introduction to Probability Theory and Its Applications},
  volume = {II},
  edition = {2},
  publisher = {John Wiley \& Sons},
  year = {1971},
  isbn = {9780471257097}
}

@article{agarwal1972,
  author = {Agarwal, Girish S.},
  title = {Fluctuation-dissipation theorems for systems in non-thermal
           equilibrium and applications},
  journal = {Zeitschrift f{\"u}r Physik},
  volume = {252}, number = {1}, pages = {25--38}, year = {1972},
  doi = {10.1007/BF01391621},
  url = {https://link.springer.com/article/10.1007/BF01391621}
}

@article{bmw2009,
  author = {Baiesi, Marco and Maes, Christian and Wynants, Bram},
  title = {Fluctuations and response of nonequilibrium states},
  journal = {Physical Review Letters},
  volume = {103}, number = {1}, pages = {010602}, year = {2009},
  doi = {10.1103/PhysRevLett.103.010602},
  eprint = {0902.3955}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/0902.3955}
}