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arXiv · 2002.09221

Self-improvement of the Bakry-Emery criterion for Poincar{\'e} inequalities and Wasserstein contraction using variable curvature bounds

Patrick Cattiaux·Max Fathi·Arnaud Guillin
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Abstract

We study Poincar{\'e} 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 Poincar{\'e} 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 Poincar{\'e} inequalities when curvature is positive but not constant.

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Patrick Cattiaux, Max Fathi, Arnaud Guillin. 2020-02-21. Self-improvement of the Bakry-Emery criterion for Poincar{\'e} inequalities and Wasserstein contraction using variable curvature bounds. https://arxiv.org/abs/2002.09221

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