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SELF-IMPROVEMENT OF THE BAKRY-EMERY CRITERION FOR POINCARÉ INEQUALITIES AND WASSERSTEIN CONTRACTION USING VARIABLE CURVATURE BOUNDS

Abstract : We study Poincaré inequalities and long-time behavior for diffusion processes on R^n under a variable curvature lower bound, in the sense of Bakry-Emery. We derive various estimates on the rate of convergence to equilibrium in L^1 optimal transport distance, as well as bounds on the constant in the Poincaré inequality in several situations of interest, including some where curvature may be negative. In particular, we prove a self-improvement of the Bakry-Emery estimate for Poincaré inequalities when curvature is positive but not constant.
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https://hal.uca.fr/hal-02486264
Contributor : Arnaud Guillin <>
Submitted on : Thursday, February 20, 2020 - 6:38:01 PM
Last modification on : Thursday, March 5, 2020 - 5:59:00 PM

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  • HAL Id : hal-02486264, version 1
  • ARXIV : 2002.09221

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Patrick Cattiaux, Max Fathi, Arnaud Guillin. SELF-IMPROVEMENT OF THE BAKRY-EMERY CRITERION FOR POINCARÉ INEQUALITIES AND WASSERSTEIN CONTRACTION USING VARIABLE CURVATURE BOUNDS. 2020. ⟨hal-02486264⟩

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