报告题目:Uniform Poincare inequalities and logarithmic Sobolev inequalities for mean field particle systems

报告人：刘伟教授（武汉大学数学与统计学院）

报告时间：2023年4月23日 14:30—15:15

报告地点：理A110

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.

报告人简介：刘伟，武汉大学数学与统计学院，教授，博士生导师，中国概率统计学会常务理事、副秘书长，中国现场统计研究会教育统计与管理分会常务理事。目前主要从事随机分析与随机算法的研究，主持国家自科面上项目和湖北省面上项目，参与承担多项国家自科重点项目，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《应用概率统计》杂志编委。

邀请人：朱佳惠