UNIFORM POINCARÉ AND LOGARITHMIC SOBOLEV INEQUALITIES FOR MEAN FIELD PARTICLES SYSTEMS

Abstract : In this paper we establish 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 [10] by means of the displacement convexity approach, or [19, 20] by Bakry-Emery technique or the recent [9] by dissipation of the Wasserstein distance.
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https://hal.uca.fr/hal-02287711
Contributor : Arnaud Guillin <>
Submitted on : Friday, September 13, 2019 - 5:15:19 PM
Last modification on : Tuesday, September 17, 2019 - 1:17:32 AM

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  • HAL Id : hal-02287711, version 1
  • ARXIV : 1909.07051

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Arnaud Guillin, Wei Liu, Liming Wu, Chaoen Zhang. UNIFORM POINCARÉ AND LOGARITHMIC SOBOLEV INEQUALITIES FOR MEAN FIELD PARTICLES SYSTEMS. 2019. ⟨hal-02287711⟩

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