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arXiv · 1909.07051

Uniform Poincar{é} and logarithmic Sobolev inequalities for mean field particles systems

Arnaud Guillin·Wei Liu·Liming Wu·Chaoen Zhang
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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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Arnaud Guillin, Wei Liu, Liming Wu, Chaoen Zhang. 2019-09-16. Uniform Poincar{é} and logarithmic Sobolev inequalities for mean field particles systems. https://arxiv.org/abs/1909.07051

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