Uniform Poincare inequalities and logarithmic Sobolev inequalities for mean field particle systems

报告人：刘伟

报告地点：腾讯会议ID:370 585 353

报告时间：2022年11月21日星期一9:00-10:30

报告摘要:

In this talk we show some explicit and sharp estimates of the spectral gap and the log-Sobolev constant for mean field particles system, uniform in the number of particles, when the confinement potential have many local minimums. Our uniform log-Sobolev inequality, based on Zegarlinski‘s theorem for Gibbs measures, allows us to obtain the exponential convergence in entropy of the McKean-Vlasov equation with an explicit rate constant, generalizing the result of Carrillo-McCann-Villani(2003) by means of the displacement convexity approach, or Malrieu(2001,2003) by Bakry-Emery technique or the recent work of Bolley-Gentil-Guillin by dissipation of the Wasserstein distance.This talk is based on a joint work with Arnaud Guillin, Liming Wu and Chaoen Zhang.

主讲人简介：

刘伟，武汉大学数学与统计学院，教授，博士生导师。1999年进入武汉大学数学基地班学习，2003年免试攻读硕士研究生(硕博连读，师从吴黎明教授)，读博期间曾在法国进行博士联合培养，2009年博士毕业留校任教。2017年至2019年受留学基金委资助在法国公派访学。目前主要从事随机分析和随机算法方面的研究，主持国家自科面上项目，参与承担多项国家自科重点项目和面上项目，在CMP、JMPA、AOAP、SPA、AIHP、Science in China 等国内外一流学术期刊发表学术论文，担任多家过国内外期刊审稿人。