Uniform Poincare inequalities and logarithmic Sobolev inequalities for mean field particle systems
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：刘伟（武汉大学）
：2023-03-03 10:00
：腾讯会议ID：767224425（无密码）
报告人：刘伟（武汉大学）
时 间：2023年3月3日上午10:00-11:30
地 点：腾讯会议ID：767224425（无密码）
内容摘要:
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.
个人简介：
刘伟，武汉大学数学与统计学院教授，博士生导师。2009年博士毕业留校任教。目前主要从事随机分析，随机算法，最优传输和机器学习方面的研究，主持国家自科面上项目，参与国家自科重点项目，在CMP、JMPA、AOAP、SPA、AIHP等一流学术期刊发表多篇学术论文。
联系人：陈娴
