Uniform Poincar{\'e} and logarithmic Sobolev inequalities for mean field particles systems
Probability
2019-09-17 v1
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.
Keywords
Cite
@article{arxiv.1909.07051,
title = {Uniform Poincar{\'e} and logarithmic Sobolev inequalities for mean field particles systems},
author = {Arnaud Guillin and Wei Liu and Liming Wu and Chaoen Zhang},
journal= {arXiv preprint arXiv:1909.07051},
year = {2019}
}