Reference : Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein ...
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Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/47901
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 mailto [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.
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http://hdl.handle.net/10993/47901
https://math.uni.lu/thalmaier/PREPRINTS/Stein-HSI.html
https://arxiv.org/abs/2108.12755

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