@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://www.jstor.org/stable/2373688}
}

@article{OttoVillani2000,
  author = {Otto, Felix and Villani, C{\'e}dric},
  title = {Generalization of an Inequality by {Talagrand} and Links with the Logarithmic {Sobolev} Inequality},
  journal = {Journal of Functional Analysis},
  volume = {173},
  number = {2},
  pages = {361--400},
  year = {2000},
  doi = {10.1006/jfan.1999.3557},
  url = {https://doi.org/10.1006/jfan.1999.3557}
}

@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},
  publisher = {Springer},
  address = {Berlin},
  pages = {177--206},
  year = {1985},
  doi = {10.1007/BFb0075847},
  url = {https://numdam.org/item/SPS_1985__19__177_0/}
}

@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},
  publisher = {Springer},
  address = {Berlin},
  pages = {120--216},
  year = {1999},
  doi = {10.1007/BFb0096511},
  url = {https://numdam.org/item/SPS_1999__33__120_0/}
}

@article{Bizeul2026,
  author = {Bizeul, Pierre},
  title = {On the log-{Sobolev} constant of log-concave vectors},
  journal = {Journal of Functional Analysis},
  volume = {290},
  number = {9},
  pages = {111368},
  year = {2026},
  doi = {10.1016/j.jfa.2026.111368},
  eprint = {2306.12997v3},
  archivePrefix = {arXiv},
  primaryClass = {math.FA},
  note = {Cited theorem numbers refer to arXiv:2306.12997v3, 16 February 2026; first posted in 2023},
  url = {https://arxiv.org/abs/2306.12997v3}
}

@article{KlartagLehec2024,
  author = {Klartag, Bo'az and Lehec, Joseph},
  title = {Isoperimetric inequalities in high-dimensional convex sets},
  journal = {Bulletin of the American Mathematical Society},
  volume = {62},
  number = {4},
  pages = {575--642},
  year = {2025},
  doi = {10.1090/bull/1869},
  eprint = {2406.01324v2},
  archivePrefix = {arXiv},
  primaryClass = {math.FA},
  note = {Cited theorem numbers refer to arXiv:2406.01324v2, 29 November 2024},
  url = {https://arxiv.org/abs/2406.01324v2}
}

@article{GuoShamaiVerdu2005,
  author = {Guo, Dongning and Shamai (Shitz), Shlomo and Verd{\'u}, Sergio},
  title = {Mutual information and minimum mean-square error in {Gaussian} channels},
  journal = {IEEE Transactions on Information Theory},
  volume = {51},
  number = {4},
  pages = {1261--1282},
  year = {2005},
  month = apr,
  doi = {10.1109/TIT.2005.844072},
  eprint = {cs/0412108v1},
  archivePrefix = {arXiv},
  note = {Cited theorem and equation numbers refer to arXiv:cs/0412108v1},
  url = {https://arxiv.org/abs/cs/0412108v1}
}

@misc{Viaclovsky2004,
  author = {Viaclovsky, Jeff},
  title = {Differential Analysis, {MIT} 18.156: Lecture Notes},
  year = {2004},
  howpublished = {MIT OpenCourseWare, Spring 2004},
  note = {Lectures 3, 10, 16, 18, 19, and 24; notes prepared from the instructor's handwritten notes by Zuoqin Wang (Lectures 0--11) and Yanir Rubinstein (Lectures 12--24)},
  url = {https://ocw.mit.edu/courses/18-156-differential-analysis-spring-2004/pages/lecture-notes/}
}

@article{Bobkov1999,
  author = {Bobkov, Sergey G.},
  title = {Isoperimetric and analytic inequalities for log-concave probability measures},
  journal = {The Annals of Probability},
  volume = {27},
  number = {4},
  pages = {1903--1921},
  year = {1999},
  doi = {10.1214/aop/1022874820},
  url = {https://doi.org/10.1214/aop/1022874820}
}

@article{Ito1951,
  author = {It{\^o}, Kiyosi},
  title = {Multiple {Wiener} integral},
  journal = {Journal of the Mathematical Society of Japan},
  volume = {3}, number = {1}, pages = {157--169}, year = {1951},
  doi = {10.2969/jmsj/00310157}
}

@article{ArakiYamagami1981,
  author = {Araki, Huzihiro and Yamagami, Shigeru},
  title = {An inequality for {Hilbert--Schmidt} norm},
  journal = {Communications in Mathematical Physics},
  volume = {81}, number = {1}, pages = {89--96}, year = {1981},
  doi = {10.1007/BF01941801}
}

@article{Beigi2013,
  author = {Beigi, Salman},
  title = {Sandwiched {R{\'e}nyi} divergence satisfies data processing inequality},
  journal = {Journal of Mathematical Physics},
  volume = {54}, number = {12}, pages = {122202}, year = {2013},
  doi = {10.1063/1.4838855},
  eprint = {1306.5920v6}, archivePrefix = {arXiv}, primaryClass = {quant-ph},
  note = {Cited theorem numbers refer to arXiv:1306.5920v6},
  url = {https://arxiv.org/abs/1306.5920v6}
}

@article{Tropp2018,
  author = {Tropp, Joel A.},
  title = {Second-order matrix concentration inequalities},
  journal = {Applied and Computational Harmonic Analysis},
  volume = {44}, number = {3}, pages = {700--736}, year = {2018},
  doi = {10.1016/j.acha.2016.07.005},
  eprint = {1504.05919}, archivePrefix = {arXiv}, primaryClass = {math.PR},
  note = {Cited section and lemma numbers refer to the author preprint revised 3 August 2016},
  url = {https://tropp.caltech.edu/papers/Tro16-Second-Order-Matrix-preprint.pdf}
}

@article{Milman2010,
  author = {Milman, Emanuel},
  title = {Isoperimetric and concentration inequalities: Equivalence under curvature lower bound},
  journal = {Duke Mathematical Journal},
  volume = {154}, number = {2}, pages = {207--239}, year = {2010},
  doi = {10.1215/00127094-2010-038},
  eprint = {0902.1560v2}, archivePrefix = {arXiv}, primaryClass = {math.DG},
  note = {Cited theorem numbers refer to arXiv:0902.1560v2, 1 December 2009},
  url = {https://arxiv.org/abs/0902.1560v2}
}

@article{KlartagPutterman2023,
  author = {Klartag, Bo'az and Putterman, Eli},
  title = {Spectral monotonicity under {Gaussian} convolution},
  journal = {Annales de la Facult\'e des Sciences de Toulouse. Math\'ematiques},
  series = {6}, volume = {32}, number = {5}, pages = {939--967}, year = {2023},
  doi = {10.5802/afst.1759},
  url = {https://www.numdam.org/item/10.5802/afst.1759.pdf}
}

@article{KimMilman2012,
  author = {Kim, Young-Heon and Milman, Emanuel},
  title = {A generalization of {Caffarelli}'s contraction theorem via (reverse) heat flow},
  journal = {Mathematische Annalen},
  volume = {354}, number = {3}, pages = {827--862}, year = {2012},
  doi = {10.1007/s00208-011-0749-x},
  eprint = {1002.0373v3}, archivePrefix = {arXiv}, primaryClass = {math.FA},
  url = {https://arxiv.org/abs/1002.0373v3}
}

@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},
  eprint = {2007.08200v2}, archivePrefix = {arXiv}, primaryClass = {math.PR},
  note = {Cited theorem and equation numbers refer to arXiv:2007.08200v2, 6 August 2021},
  url = {https://arxiv.org/abs/2007.08200v2}
}

@article{ChenEldan2022,
  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}, year = {2025},
  doi = {10.1215/00127094-2024-0063},
  eprint = {2203.04163v2}, archivePrefix = {arXiv}, primaryClass = {math.PR},
  note = {Cited section and equation numbers refer to arXiv:2203.04163v2, 6 June 2022},
  url = {https://arxiv.org/abs/2203.04163v2}
}

@article{Lieb1973,
  author = {Lieb, Elliott H.},
  title = {Convex trace functions and the {Wigner--Yanase--Dyson} conjecture},
  journal = {Advances in Mathematics},
  volume = {11}, number = {3}, pages = {267--288}, year = {1973},
  doi = {10.1016/0001-8708(73)90011-X},
  url = {https://www.numdam.org/item/RCP25_1973__19__A4_0/}
}

@article{Rothaus1986,
  author = {Rothaus, O. S.},
  title = {Hypercontractivity and the {Bakry--Emery} criterion for compact {Lie} groups},
  journal = {Journal of Functional Analysis},
  volume = {65}, number = {3}, pages = {358--367}, year = {1986},
  doi = {10.1016/0022-1236(86)90025-X}
}