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

Li-Juan Cheng Orcid Logo, Anton Thalmaier Orcid Logo, 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....

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Published in: Journal of Functional Analysis
ISSN: 0022-1236
Published: Elsevier BV 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa63390
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first_indexed 2023-05-10T10:06:52Z
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spelling v2 63390 2023-05-10 Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance 6734caa6d9a388bd3bd8eb0a1131d0de Feng-yu Wang Feng-yu Wang true false 2023-05-10 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. Journal Article Journal of Functional Analysis 285 5 109997 Elsevier BV 0022-1236 Relative entropy, Fisher information, Stein discrepancy, Wasserstein distance 1 9 2023 2023-09-01 10.1016/j.jfa.2023.109997 COLLEGE NANME COLLEGE CODE Swansea University 2024-07-29T14:21:39.1405030 2023-05-10T11:03:48.3778305 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Li-Juan Cheng 0000-0001-6778-2770 1 Anton Thalmaier 0000-0002-0567-2469 2 Feng-yu Wang 3 63390__27441__0d20141fb0aa49059fc3654d95584443.pdf 63390.pdf 2023-05-11T13:37:47.8824742 Output 240292 application/pdf Accepted Manuscript true 2024-05-03T00:00:00.0000000 Distributed under the terms of a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). true eng https://creativecommons.org/licenses/by-nc-nd/4.0/
title Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance
spellingShingle Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance
Feng-yu Wang
title_short Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance
title_full Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance
title_fullStr Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance
title_full_unstemmed Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance
title_sort Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance
author_id_str_mv 6734caa6d9a388bd3bd8eb0a1131d0de
author_id_fullname_str_mv 6734caa6d9a388bd3bd8eb0a1131d0de_***_Feng-yu Wang
author Feng-yu Wang
author2 Li-Juan Cheng
Anton Thalmaier
Feng-yu Wang
format Journal article
container_title Journal of Functional Analysis
container_volume 285
container_issue 5
container_start_page 109997
publishDate 2023
institution Swansea University
issn 0022-1236
doi_str_mv 10.1016/j.jfa.2023.109997
publisher Elsevier BV
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
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description 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.
published_date 2023-09-01T14:21:38Z
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score 11.035634

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