@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 = {\href{https://doi.org/10.1103/PhysRevLett.35.1792}{doi:10.1103/PhysRevLett.35.1792}}
}

@article{BB2019,
  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 = {\href{https://doi.org/10.1016/j.jfa.2019.01.007}{doi:10.1016/j.jfa.2019.01.007}.
    Preprint: \href{https://arxiv.org/abs/1712.03676v2}{arXiv:1712.03676v2}}
}

@article{EKZ2022,
  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 = {\href{https://doi.org/10.1007/s00440-021-01085-x}{doi:10.1007/s00440-021-01085-x}.
    Preprint: \href{https://arxiv.org/abs/2007.08200v2}{arXiv:2007.08200v2}}
}

@article{CE2025,
  author = {Chen, Yuansi and Eldan, Ronen},
  title = {Localization schemes: A framework for proving mixing bounds for {Markov} chains},
  journal = {Duke Mathematical Journal},
  volume = {174},
  number = {8},
  pages = {1431--1510},
  year = {2025},
  doi = {10.1215/00127094-2024-0063},
  note = {\href{https://doi.org/10.1215/00127094-2024-0063}{doi:10.1215/00127094-2024-0063}.
    Preprint version of June 6, 2022: \href{https://arxiv.org/abs/2203.04163v2}{arXiv:2203.04163v2}}
}

@inproceedings{AKV2024,
  author = {Anari, Nima and Koehler, Frederic and Vuong, Thuy-Duong},
  title = {Trickle-Down in Localization Schemes and Applications},
  booktitle = {Proceedings of the 56th Annual ACM Symposium on Theory of Computing},
  series = {STOC 2024},
  pages = {1094--1105},
  publisher = {Association for Computing Machinery},
  year = {2024},
  doi = {10.1145/3618260.3649622},
  note = {\href{https://doi.org/10.1145/3618260.3649622}{doi:10.1145/3618260.3649622}.
    Full preprint: \href{https://arxiv.org/abs/2407.16104v1}{arXiv:2407.16104v1}}
}

@misc{Wang2026,
  author = {Wang, Sihan},
  title = {Optimal Mixing of {Glauber} Dynamics for the {Sherrington--Kirkpatrick} Model at {$\beta<1/2$}},
  year = {2026},
  howpublished = {\href{https://arxiv.org/abs/2608.22159v2}{arXiv:2608.22159v2}},
  note = {Version of 28 August 2026}
}

@misc{SKGap,
  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}
}

@article{Eldan2013,
 author={Eldan, Ronen},
 title={Thin shell implies spectral gap up to polylog via a stochastic localization scheme},
 journal={Geometric and Functional Analysis}, volume={23}, number={2}, pages={532--569}, year={2013},
 note={\href{https://doi.org/10.1007/s00039-013-0214-y}{doi:10.1007/s00039-013-0214-y}}
}
@misc{ElAlaouiMontanari2021,
 author={El Alaoui, Ahmed and Montanari, Andrea},
 title={An Information-Theoretic View of Stochastic Localization}, year={2021},
 note={\href{https://arxiv.org/abs/2109.00709v2}{arXiv:2109.00709v2}, September 9, 2021}
}
@article{Lehec2013,
 author={Lehec, Joseph}, title={Representation formula for the entropy and functional inequalities},
 journal={Annales de l'Institut Henri Poincar\'e, Probabilit\'es et Statistiques},
 volume={49}, number={3}, pages={885--899}, year={2013},
 note={\href{https://doi.org/10.1214/11-AIHP464}{doi:10.1214/11-AIHP464}}
}
@article{Gross1975,
 author={Gross, Leonard}, title={Logarithmic {Sobolev} inequalities},
 journal={American Journal of Mathematics}, volume={97}, number={4}, pages={1061--1083}, year={1975},
 note={\href{https://www.jstor.org/stable/2373688}{JSTOR:2373688}}
}
@article{Bolthausen2014,
 author={Bolthausen, Erwin}, title={An iterative construction of solutions of the {TAP} equations for the {Sherrington--Kirkpatrick} model},
 journal={Communications in Mathematical Physics}, volume={325}, number={1}, pages={333--366}, year={2014},
 note={\href{https://doi.org/10.1007/s00220-013-1862-3}{doi:10.1007/s00220-013-1862-3}.
   Preprint: \href{https://arxiv.org/abs/1201.2891v1}{arXiv:1201.2891v1}, January 13, 2012}
}
@article{Celentano2024,
 author={Celentano, Michael}, title={{Sudakov--Fernique} post-{AMP}, and a new proof of the local convexity of the {TAP} free energy},
 journal={Annals of Probability}, volume={52}, number={3}, pages={923--954}, year={2024},
 note={\href{https://doi.org/10.1214/23-AOP1675}{doi:10.1214/23-AOP1675}.
   Preprint: \href{https://arxiv.org/abs/2208.09550v1}{arXiv:2208.09550v1}, August 19, 2022}
}
@article{Vitale2000,
 author={Vitale, Richard A.}, title={Some comparisons for {Gaussian} processes},
 journal={Proceedings of the American Mathematical Society}, volume={128}, number={10}, pages={3043--3046}, year={2000},
 note={\href{https://doi.org/10.1090/S0002-9939-00-05367-3}{doi:10.1090/S0002-9939-00-05367-3}}
}

@article{ABXY2024,
 author={Adhikari, Arka and Brennecke, Christian and Xu, Changji and Yau, Horng-Tzer},
 title={Spectral gap estimates for mixed {$p$}-spin models at high temperature},
 journal={Probability Theory and Related Fields}, volume={189}, number={3--4}, pages={879--907}, year={2024},
 note={\href{https://doi.org/10.1007/s00440-024-01261-9}{doi:10.1007/s00440-024-01261-9}}
}
@inproceedings{AJKPV2022,
 author={Anari, Nima and Jain, Vishesh and Koehler, Frederic and Pham, Huy Tuan and Vuong, Thuy-Duong},
 title={Entropic independence: optimal mixing of down-up random walks},
 booktitle={Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing},
 pages={1418--1430}, year={2022},
 note={\href{https://doi.org/10.1145/3519935.3520048}{doi:10.1145/3519935.3520048}. Full Ising proof: \href{https://arxiv.org/abs/2106.04105v2}{arXiv:2106.04105v2}}
}
@misc{BLO2026,
 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 {$\beta\leq\frac12+\varepsilon$}},
 year={2026},
 note={\href{https://arxiv.org/abs/2609.13138v1}{arXiv:2609.13138v1}, September 11, 2026}
}

@article{ChenSaloffCoste2013,
 author={Chen, Guan-Yu and Saloff-Coste, Laurent},
 title={Comparison of cutoffs between lazy walks and {Markovian} semigroups},
 journal={Journal of Applied Probability}, volume={50}, number={4}, pages={943--959}, year={2013},
 doi={10.1239/jap/1389370092},
 note={\href{https://doi.org/10.1239/jap/1389370092}{doi:10.1239/jap/1389370092}.
   Preprint: \href{https://arxiv.org/abs/1304.4587v1}{arXiv:1304.4587v1}}
}
@book{NicaSpeicher2006,
 author={Nica, Alexandru and Speicher, Roland},
 title={Lectures on the Combinatorics of Free Probability},
 publisher={Cambridge University Press}, year={2006},
 note={\href{https://rolandspeicher.com/wp-content/uploads/2020/06/nica-speicher-book.pdf}{Author-hosted full text}}
}
@misc{Male2010,
 author={Male, Camille},
 title={The norm of polynomials in large random and deterministic matrices},
 year={2010},
 note={\href{https://arxiv.org/abs/1004.4155v5}{arXiv:1004.4155v5}, May 18, 2011; Theorem 1.6}
}

@article{Salez2024,
 author={Salez, Justin},
 title={Cutoff for non-negatively curved {Markov} chains},
 journal={Journal of the European Mathematical Society},
 volume={26}, number={11}, pages={4375--4392}, year={2024},
 doi={10.4171/JEMS/1348},
 note={\href{https://doi.org/10.4171/JEMS/1348}{doi:10.4171/JEMS/1348};
 preprint \href{https://arxiv.org/abs/2102.05597v2}{arXiv:2102.05597v2}}
}

@article{ALR1987,
  author = {Aizenman, Michael and Lebowitz, Joel L. and Ruelle, David},
  title = {Some rigorous results on the {Sherrington--Kirkpatrick} spin glass model},
  journal = {Communications in Mathematical Physics},
  volume = {112}, number = {1}, pages = {3--20}, year = {1987},
  doi = {10.1007/BF01217677},
  note = {\href{https://doi.org/10.1007/BF01217677}{doi:10.1007/BF01217677}}
}
@article{Guerra2003,
  author = {Guerra, Francesco},
  title = {Broken replica symmetry bounds in the mean field spin glass model},
  journal = {Communications in Mathematical Physics},
  volume = {233}, number = {1}, pages = {1--12}, year = {2003},
  doi = {10.1007/s00220-002-0773-5},
  note = {\href{https://doi.org/10.1007/s00220-002-0773-5}{doi:10.1007/s00220-002-0773-5}.
    Preprint: \href{https://arxiv.org/abs/cond-mat/0205123v1}{arXiv:cond-mat/0205123v1}}
}

@article{Panchenko2010DS,
  author = {Panchenko, Dmitry},
  title = {On the {Dovbysh--Sudakov} representation result},
  journal = {Electronic Communications in Probability},
  volume = {15}, pages = {330--338}, year = {2010},
  doi = {10.1214/ECP.v15-1562},
  note = {\href{https://doi.org/10.1214/ECP.v15-1562}{doi:10.1214/ECP.v15-1562}}
}

@article{Haagerup1979,
  author = {Haagerup, Uffe},
  title = {An Example of a Non Nuclear {$C^*$}-Algebra, which has the Metric Approximation Property},
  journal = {Inventiones Mathematicae},
  volume = {50}, pages = {279--293}, year = {1979},
  doi = {10.1007/BF01410082},
  note = {\href{https://doi.org/10.1007/BF01410082}{doi:10.1007/BF01410082}}
}

@misc{Giraud2021,
  author = {Giraud, Christophe},
  title = {Introduction to High-Dimensional Statistics},
  year = {2021},
  note = {Author-hosted second-edition manuscript, Exercise 1.6.7.
    \href{https://www.imo.universite-paris-saclay.fr/~giraud/Orsay/Bookv3.pdf}{Full text}}
}