報告題目： Uniform Poincare inequalities and logarithmic Sobolev inequalities for mean field particle systems
報 告 人：劉偉 教授 武漢大學數學與統計學院
報告時間：2023年3月13日 16：00-17：00
報告地點：數學樓第二報告廳
校内聯系人：韓月才 hanyc@jlu.edu.cn
報告摘要：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.
報告人簡介：劉偉，武漢大學數學與統計學院，教授，博士生導師，中國概率統計學會常務理事、副秘書長。目前主要從事随機分析和随機算法方面的研究，主持國家自科面上項目和湖北省面上項目，參與承擔多項國家自科重點項目和面上項目，在CMP、JMPA、AOAP、SPA、AIHP、Science in China 等國内外一流學術期刊發表學術論文，擔任《應用概率統計》雜志編委和多家國内外期刊審稿人。
