Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance

English

Cheng, Li-Juan[Zhejiang University of Technology > Department of Applied Mathematics]

Thalmaier, Anton[University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]

Wang, Feng-Yu[Tianjin University > Center for Applied Mathematics]

25-Aug-2021

26

No

[en] For a complete connected Riemannian manifold M let V∊ C^2(M) be such that µ(dx)=exp(-V(x))vol(dx) is a probability measure on M. Taking µ as reference measure, we derive 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.