Article (Scientific journals)
Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance
Cheng, Li-Juan; Thalmaier, Anton; Wang, Feng-Yu
2023In Journal of Functional Analysis, 285 (5), p. 109997
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Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
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
External co-authors :
yes
Language :
English
Title :
Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance
Publication date :
01 September 2023
Journal title :
Journal of Functional Analysis
ISSN :
1096-0783
Publisher :
Elsevier, Atlanta, Georgia
Volume :
285
Issue :
5
Pages :
109997
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 01 September 2021

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