报告题目：Some Inequalities on Riemannian Manifolds Linking Entropy Fisher Information, Stein Discrepancy and Wasserstein Distance

报告时间：2022-12-30 14:30 - 15:30

报告人：程丽娟 副教授  杭州师范大学

腾讯会议ID：980 459 070

Abstract：For a complete connected Riemannian manifold M let V∈C^{2 (M)} be such that μ(dx)=e^{(-V(x) )} vol(dx) is a probability measure on M. Taking μ as reference measure, in this talk, I will introduce some inequalities for probability measures on M linking relative entropy, Fisher information, Stein discrepancy and Wasserstein distance. These inequalities strengthen in particular the famous log-Sobolev and transportation-cost inequality and extend the so-called Entropy/Stein-discrepancy/Information (HSI) inequality established by Ledoux, Nourdin and Peccati (2015) for the standard Gaussian measure on Euclidean space to the setting of Riemannian manifolds. This talk is based on a joint work with Anton Thalmaier and Feng-Yu Wang.