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

邀请人：李童庆、薄立军

报告时间：2022年11月21日（周一）15：00-16：00

腾讯会议ID：267-420-481，密码：123456

报告人简介：刘伟，武汉大学伟德国际BETVlCTOR教授、博士生导师。2007年本科毕业于武汉大学，2009年于武汉大学获得博士学位。主持国家自然科学面上项目，参与承担多项国家自然科学重点项目和面上项目。主要从事随机分析、大偏差、泛函不等式的研究，已在Ann. Appl. Probab., Comm. Math. Phys., Stochastic Process. Appl., J. Math. Pures Appl.等国际权威数学期刊发表学术论文50余篇。

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.