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Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance
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Anton Thalmaier ,
Feng-yu Wang
Journal of Functional Analysis, Volume: 285, Issue: 5, Start page: 109997
Swansea University Author: Feng-yu Wang
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DOI (Published version): 10.1016/j.jfa.2023.109997
Abstract
For a complete connected Riemannian manifold M let V ∈ C2(M) be such that μ(dx) =e−V(x) vol(dx) is a probability measure on M. Taking μ as reference measure, we derive in-equalities for probability measures on M linking relative entropy, Fisher information, Steindiscrepancy and Wasserstein distance....
| Published in: | Journal of Functional Analysis |
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| ISSN: | 0022-1236 |
| Published: |
Elsevier BV
2023
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa63390 |
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| Abstract: |
For a complete connected Riemannian manifold M let V ∈ C2(M) be such that μ(dx) =e−V(x) vol(dx) is a probability measure on M. Taking μ as reference measure, we derive in-equalities for probability measures on M linking relative entropy, Fisher information, Steindiscrepancy and Wasserstein distance. These inequalities strengthen in particular the fa-mous 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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| Keywords: |
Relative entropy, Fisher information, Stein discrepancy, Wasserstein distance |
| College: |
Faculty of Science and Engineering |
| Issue: |
5 |
| Start Page: |
109997 |