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      Uniform Poincar{\'e} and logarithmic Sobolev inequalities for mean field particles systems

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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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          Most cited references 17

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          Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality

           F Otto,  C Villani (2000)
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            Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates

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              Hypercontractivity of Hamilton–Jacobi equations

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                Author and article information

                Journal
                16 September 2019
                Article
                1909.07051

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                math.PR
                ccsd

                Probability

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