{"title":"Uniform-in-$N$ log-Sobolev inequality for the mean-field Langevin dynamics with convex energy","authors":"Sinho Chewi, Atsushi Nitanda, Matthew S. Zhang","doi":"arxiv-2409.10440","DOIUrl":null,"url":null,"abstract":"We establish a log-Sobolev inequality for the stationary distribution of\nmean-field Langevin dynamics with a constant that is independent of the number\nof particles $N$. Our proof proceeds by establishing the existence of a\nLipschitz transport map from the standard Gaussian measure via the reverse heat\nflow of Kim and Milman.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"48 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10440","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We establish a log-Sobolev inequality for the stationary distribution of
mean-field Langevin dynamics with a constant that is independent of the number
of particles $N$. Our proof proceeds by establishing the existence of a
Lipschitz transport map from the standard Gaussian measure via the reverse heat
flow of Kim and Milman.
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