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تسجيل مستخدم جديدSelf-improvement of the Bakry-Emery criterion for Poincar{e} inequalities and Wasserstein contraction using variable curvature bounds
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تأليف
Patrick Cattiaux
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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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