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3月13日 16：00-17：00
报告地点：数学楼第二报告厅
校内联系人：韩月才 hanyc@jlu.edu.cn
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。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和湖北省面上项目，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《应用概率统计》杂志编委和多家国内外期刊审稿人。
