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必威、所2023年系列学术活动(第003场):刘伟 教授 武汉大学

发表于: 2023-03-11   点击: 

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。