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

Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance
by Li-Juan Cheng, Anton Thalmaier and Feng-Yu Wang

Abstract
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.

Journal of Functional Analysis 285 (2023), no. 5, 109997

https://doi.org/10.1016/j.jfa.2023.109997

The preprint version is available here:

PDF (1036K)

Li-Juan Cheng	chenglj@zjut.edu.cn
Anton Thalmaier	anton.thalmaier@uni.lu
Feng-Yu Wang	wangfy@tju.edu.cn

Back to Homepage

Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance by Li-Juan Cheng, Anton Thalmaier and Feng-Yu Wang

Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance
by Li-Juan Cheng, Anton Thalmaier and Feng-Yu Wang