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Uniform Poincare inequalities and logarithmic Sobolev inequalities for mean field particle systems

 
Title:
Uniform Poincare inequalities and logarithmic Sobolev inequalities for mean field particle systems
Speaker:
刘伟 副教授,武汉大学
Inviter: 李向东 研究员
Time & Venue:

2022.1.20 14:30 腾讯会议号:180-803-183

Abstract:

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.

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Affiliation:  

学术报告中国科学院数学与系统科学研究院应用数学研究所
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