论文标题
使用可变曲率界限的Bakry-Emery {é}不平等和Wasserstein收缩的自我改善
Self-improvement of the Bakry-Emery criterion for Poincar{é} inequalities and Wasserstein contraction using variable curvature bounds
论文作者
论文摘要
我们研究了bakry emery的意义，在可变的曲率下限下，在可变曲率下限下，poincar {é}的不平等和长期行为。我们得出了对l^1最佳传输距离的收敛速率的各种估计，以及在几种感兴趣的情况下，庞加尔{é}不平等的常数，包括一些曲率可能为负的情况。特别是，当曲率是积极但不是恒定的时，我们证明了对Poincar {é}不平等的Bakry-Emery估计的自我完善。
We study Poincar{é} 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{é} 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{é} inequalities when curvature is positive but not constant.
