10月2日概率统计系列讲座：
报告题目：【Uniform Poincar\'e Inequalities and Logarithmic Sobolev Inequalities for Mean Field Particle Systems】
时间：2020年10月2日 (星期五) 上午08:00
地点：腾讯会议（会议ID：978 611 814）
主讲：武汉大学教授，刘伟
主办：数学与信息学院
参加对象：统计系老师与学生
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.