Uniform Poincare inequalities and logarithmic Sobolev inequalities for mean field particle systems
时间：2022-05-09
阅读量：511次
- 演讲人： 刘伟（武汉大学 副教授）
- 时间：2022年05月15日 周日 16:00
- 地点：腾讯会议 436-702-636
- 主办单位：数据科学研究中心，统计学研究所
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，副教授，近年来主要研究平均场交互作用粒子系统和McKean-Vlasov方程的相关问题。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、AAP、SPA、AIHP、Science in China 等国内外期刊发表学术论文，担任SPA等多家过国内外期刊的审稿人。
联系人：苏中根（suzhonggen@zju.edu.cn）
欢迎参加！