Self-improvement of the Bakry-Emery criterion for Poincaré inequalities and Wasserstein contraction using variable curvature bounds. (English. French summary) Zbl 1498.60324
Summary: We study Poincaré inequalities and long-time behavior for diffusion processes on \(\mathbb{R}^n\) 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.
MSC:
| 60J60 | Diffusion processes |
| 58J65 | Diffusion processes and stochastic analysis on manifolds |
| 47D07 | Markov semigroups and applications to diffusion processes |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
| 60E15 | Inequalities; stochastic orderings |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
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