Article Dans Une Revue The Annals of Applied Probability Année : 2022

UNIFORM POINCARÉ AND LOGARITHMIC SOBOLEV INEQUALITIES FOR MEAN FIELD PARTICLES SYSTEMS

Résumé

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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hal-02287711 , version 1 (13-09-2019)

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Arnaud Guillin, Wei Liu, Liming Wu, Chaoen Zhang. UNIFORM POINCARÉ AND LOGARITHMIC SOBOLEV INEQUALITIES FOR MEAN FIELD PARTICLES SYSTEMS. The Annals of Applied Probability, 2022, 32 (3), ⟨10.1214/21-AAP1707⟩. ⟨hal-02287711⟩
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