@article{sk1975,
  author = {Sherrington, David and Kirkpatrick, Scott},
  title = {Solvable Model of a Spin-Glass},
  journal = {Physical Review Letters},
  volume = {35},
  number = {26},
  pages = {1792--1796},
  year = {1975},
  doi = {10.1103/PhysRevLett.35.1792},
  note = {\url{https://doi.org/10.1103/PhysRevLett.35.1792}}
}

@article{dumitriuEdelman2002,
  author = {Dumitriu, Ioana and Edelman, Alan},
  title = {Matrix models for beta ensembles},
  journal = {Journal of Mathematical Physics},
  volume = {43},
  number = {11},
  pages = {5830--5847},
  year = {2002},
  doi = {10.1063/1.1507823},
  note = {\url{https://doi.org/10.1063/1.1507823}; preprint \url{https://arxiv.org/abs/math-ph/0206043v1}}
}

@misc{skgapcompanion,
  author = {{OpenAI}},
  title = {{A spectral gap throughout the high-temperature Sherrington--Kirkpatrick phase}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-spectral-gap-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase-September-24-2026/main.pdf}{OAI:A-spectral-gap-throughout-the-high-temperature-Sherrington-Kirkpatrick-phase-September-24-2026}},
  year = {2026},
  note = {Theorem 1.1}
}

@article{bauerschmidtBodineau2019,
  author = {Bauerschmidt, Roland and Bodineau, Thierry},
  title = {A very simple proof of the {LSI} for high temperature spin systems},
  journal = {Journal of Functional Analysis},
  volume = {276},
  number = {8},
  pages = {2582--2588},
  year = {2019},
  doi = {10.1016/j.jfa.2019.01.007},
  note = {\url{https://doi.org/10.1016/j.jfa.2019.01.007}; preprint \url{https://arxiv.org/abs/1712.03676v2}}
}

@article{eldanKoehlerZeitouni2022,
  author = {Eldan, Ronen and Koehler, Frederic and Zeitouni, Ofer},
  title = {A spectral condition for spectral gap: fast mixing in high-temperature {Ising} models},
  journal = {Probability Theory and Related Fields},
  volume = {182},
  number = {3--4},
  pages = {1035--1051},
  year = {2022},
  doi = {10.1007/s00440-021-01085-x},
  note = {\url{https://doi.org/10.1007/s00440-021-01085-x}; preprint \url{https://arxiv.org/abs/2007.08200v2}}
}

@article{kirkpatrickSherrington1978,
  author = {Kirkpatrick, Scott and Sherrington, David},
  title = {Infinite-ranged models of spin-glasses},
  journal = {Physical Review B}, volume = {17}, pages = {4384--4403},
  year = {1978}, doi = {10.1103/PhysRevB.17.4384},
  note = {\url{https://doi.org/10.1103/PhysRevB.17.4384}}
}
@article{sompolinskyZippelius1981,
  author = {Sompolinsky, Haim and Zippelius, Annette},
  title = {Dynamic Theory of the Spin-Glass Phase},
  journal = {Physical Review Letters}, volume = {47}, pages = {359--362},
  year = {1981}, doi = {10.1103/PhysRevLett.47.359},
  note = {\url{https://doi.org/10.1103/PhysRevLett.47.359}}
}
@article{sompolinskyZippelius1982,
  author = {Sompolinsky, Haim and Zippelius, Annette},
  title = {Relaxational dynamics of the {Edwards--Anderson} model and the mean-field theory of spin-glasses},
  journal = {Physical Review B}, volume = {25}, pages = {6860--6875},
  year = {1982}, doi = {10.1103/PhysRevB.25.6860},
  note = {\url{https://doi.org/10.1103/PhysRevB.25.6860}}
}
@article{billoireCampbell2011,
  author = {Billoire, Alain and Campbell, I. A.},
  title = {Dynamics in the {Sherrington--Kirkpatrick Ising} spin glass at and above {$T_g$}},
  journal = {Physical Review B}, volume = {84}, pages = {054442},
  year = {2011}, doi = {10.1103/PhysRevB.84.054442},
  eprint = {1105.1902}, archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.1103/PhysRevB.84.054442}}
}
@article{ramirezRiderVirag2011,
  author = {Ram{\'i}rez, Jos{\'e} and Rider, Brian and Vir{\'a}g, B{\'a}lint},
  title = {Beta ensembles, stochastic {Airy} spectrum, and a diffusion},
  journal = {Journal of the American Mathematical Society},
  volume = {24}, number = {4}, pages = {919--944}, year = {2011},
  doi = {10.1090/S0894-0347-2011-00703-0},
  eprint = {math/0607331}, archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.1090/S0894-0347-2011-00703-0}}
}
@article{ledouxRider2010,
  author = {Ledoux, Michel and Rider, Brian},
  title = {Small deviations for beta ensembles},
  journal = {Electronic Journal of Probability}, volume = {15},
  number = {41}, pages = {1319--1343}, year = {2010},
  doi = {10.1214/EJP.v15-798}, eprint = {0912.5040}, archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.1214/EJP.v15-798}}
}

@article{kosterlitzThoulessJones1976,
  author = {Kosterlitz, J. M. and Thouless, D. J. and Jones, Raymund C.},
  title = {Spherical Model of a Spin-Glass},
  journal = {Physical Review Letters},
  volume = {36},
  number = {20},
  pages = {1217--1220},
  year = {1976},
  doi = {10.1103/PhysRevLett.36.1217},
  note = {\url{https://doi.org/10.1103/PhysRevLett.36.1217}}
}

@article{baikLee2016,
  author = {Baik, Jinho and Lee, Ji Oon},
  title = {Fluctuations of the Free Energy of the Spherical {Sherrington--Kirkpatrick} Model},
  journal = {Journal of Statistical Physics},
  volume = {165},
  pages = {185--224},
  year = {2016},
  doi = {10.1007/s10955-016-1610-0},
  eprint = {1505.07349},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  note = {\url{https://doi.org/10.1007/s10955-016-1610-0}}
}

@article{landon2022,
  author = {Landon, Benjamin},
  title = {Free energy fluctuations of the two-spin spherical {SK} model at critical temperature},
  journal = {Journal of Mathematical Physics},
  volume = {63},
  number = {3},
  pages = {033301},
  year = {2022},
  doi = {10.1063/5.0054298},
  eprint = {2010.06691},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  note = {\url{https://doi.org/10.1063/5.0054298}}
}

@article{bhattacharyaSen2016,
  author = {Bhattacharya, Bhaswar B. and Sen, Subhabrata},
  title = {High Temperature Asymptotics of Orthogonal Mean-Field Spin Glasses},
  journal = {Journal of Statistical Physics},
  volume = {162},
  number = {1},
  pages = {63--80},
  year = {2016},
  doi = {10.1007/s10955-015-1406-7},
  eprint = {1507.05067},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  note = {\url{https://doi.org/10.1007/s10955-015-1406-7}}
}

@article{bingham1974,
  author = {Bingham, Christopher},
  title = {An Antipodally Symmetric Distribution on the Sphere},
  journal = {The Annals of Statistics},
  volume = {2},
  number = {6},
  pages = {1201--1225},
  year = {1974},
  doi = {10.1214/aos/1176342874},
  note = {\url{https://doi.org/10.1214/aos/1176342874}}
}

@article{kumeWood2005,
  author = {Kume, A. and Wood, Andrew T. A.},
  title = {Saddlepoint approximations for the {Bingham} and {Fisher--Bingham} normalising constants},
  journal = {Biometrika},
  volume = {92},
  number = {2},
  pages = {465--476},
  year = {2005},
  doi = {10.1093/biomet/92.2.465},
  note = {\url{https://doi.org/10.1093/biomet/92.2.465}}
}

@article{kumePrestonWood2013,
  author = {Kume, A. and Preston, S. P. and Wood, Andrew T. A.},
  title = {Saddlepoint approximations for the normalizing constant of {Fisher--Bingham} distributions on products of spheres and {Stiefel} manifolds},
  journal = {Biometrika},
  volume = {100},
  number = {4},
  pages = {971--984},
  year = {2013},
  doi = {10.1093/biomet/ast021},
  note = {\url{https://doi.org/10.1093/biomet/ast021}}
}

@misc{duHuang2026FreeEnergy,
  author = {Du, Hang and Huang, Brice},
  title = {Fluctuations of the {Sherrington--Kirkpatrick} free energy at critical temperature},
  year = {2026},
  eprint = {2607.02172},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  note = {Version 2, July 8, 2026. \url{https://arxiv.org/abs/2607.02172v2}},
  doi = {10.48550/arXiv.2607.02172},
  url = {https://arxiv.org/abs/2607.02172v2}
}

@misc{duHuang2026Overlap,
  author = {Du, Hang and Huang, Brice},
  title = {Overlap distribution of the critical {Sherrington--Kirkpatrick} model},
  year = {2026},
  eprint = {2608.08752},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  note = {Version 1, August 9, 2026. \url{https://arxiv.org/abs/2608.08752v1}},
  doi = {10.48550/arXiv.2608.08752},
  url = {https://arxiv.org/abs/2608.08752v1}
}

@incollection{BobkovNaumovUlyanov2021,
 author = {Bobkov, Sergey G. and Naumov, Alexey A. and Ulyanov, Vladimir V.},
 title = {Two--Sided Bounds for {PDF}'s Maximum of a Sum of Weighted Chi-square Variables},
 booktitle = {Recent Developments in Stochastic Methods and Applications},
 editor = {Shiryaev, Albert N. and Samouylov, Konstantin E. and Kozyrev, Dmitry V.},
 series = {Springer Proceedings in Mathematics and Statistics},
 volume = {371},
 pages = {178--189},
 publisher = {Springer},
 year = {2021},
 doi = {10.1007/978-3-030-83266-7_13},
  note = {\url{https://doi.org/10.1007/978-3-030-83266-7_13}}
}

@article{NourdinPoly2012SecondChaos,
 author = {Nourdin, Ivan and Poly, Guillaume},
 title = {Convergence in law in the second {Wiener/Wigner} chaos},
 journal = {Electronic Communications in Probability},
 volume = {17},
 number = {36},
 pages = {1--12},
 year = {2012},
 doi = {10.1214/ECP.v17-2023},
  note = {\url{https://doi.org/10.1214/ECP.v17-2023}}
}

@article{NourdinPoly2012Erratum,
 author = {Nourdin, Ivan and Poly, Guillaume},
 title = {Erratum: Convergence in law in the second {Wiener/Wigner} chaos},
 journal = {Electronic Communications in Probability},
 volume = {17},
 number = {54},
 pages = {1--3},
 year = {2012},
 doi = {10.1214/ECP.v17-2383},
  note = {\url{https://doi.org/10.1214/ECP.v17-2383}}
}

@article{Chen2013CavityLocal,
  author = {Chen, Wei-Kuo},
  title = {Central limit theorems for cavity and local fields of the {Sherrington--Kirkpatrick} model},
  journal = {Electronic Journal of Probability},
  volume = {18},
  number = {2},
  pages = {1--25},
  year = {2013},
  doi = {10.1214/EJP.v18-1763},
  note = {\url{https://doi.org/10.1214/EJP.v18-1763}}
}
@article{Chatterjee2010Stein,
  author = {Chatterjee, Sourav},
  title = {Spin glasses and {Stein}'s method},
  journal = {Probability Theory and Related Fields},
  volume = {148},
  pages = {567--600},
  year = {2010},
  doi = {10.1007/s00440-009-0240-8},
  note = {\url{https://doi.org/10.1007/s00440-009-0240-8}}
}
@book{Talagrand2011MeanFieldI,
  author = {Talagrand, Michel},
  title = {Mean Field Models for Spin Glasses. Volume I: Basic Examples},
  publisher = {Springer},
  address = {Berlin, Heidelberg},
  year = {2011},
  doi = {10.1007/978-3-642-15202-3},
  note = {\url{https://doi.org/10.1007/978-3-642-15202-3}}
}


@misc{criticalmixingcompanion,
  author = {{OpenAI}},
  title = {{Critical mixing in the Sherrington--Kirkpatrick model}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Critical-mixing-in-the-Sherrington-Kirkpatrick-model-September-25-2026/paper.pdf}{OAI:Critical-mixing-in-the-Sherrington-Kirkpatrick-model-September-25-2026}},
  year = {2026},
  note = {Theorem 1.1}
}

@article{comets1996,
  author = {Comets, Francis},
  title = {A spherical bound for the {Sherrington--Kirkpatrick} model},
  journal = {Ast\'erisque},
  volume = {236},
  pages = {103--108},
  year = {1996},
  doi = {10.24033/ast.331},
  note = {\url{https://doi.org/10.24033/ast.331}}
}

@misc{wang2026SKMixing,
  author = {Wang, Sihan},
  title = {Optimal Mixing of Glauber Dynamics for the {Sherrington--Kirkpatrick} Model at {$\beta<1/2$}},
  year = {2026},
  eprint = {2608.22159},
  archivePrefix = {arXiv},
  note = {Version 2, August 28, 2026. \url{https://arxiv.org/abs/2608.22159v2}}
}

@misc{bobanLiOveisGharan2026SK,
  author = {Boban, Mathews and Li, Anqi and Oveis Gharan, Shayan},
  title = {Rank-1-perturbed trickledown theorems: Mixing time of Glauber dynamics for the {Sherrington--Kirkpatrick} model up to {$\beta\le\frac12+\varepsilon$}},
  year = {2026},
  eprint = {2609.13138},
  archivePrefix = {arXiv},
  note = {Version 1, September 11, 2026. \url{https://arxiv.org/abs/2609.13138v1}}
}