Square Root Convexity of Fisher Information along Heat Flow in Dimension Two

Recently, Ledoux, Nair, and Wang proved that the Fisher information along the heat flow is log-convex in dimension one, that is [Formula: see text] for [Formula: see text] , where [Formula: see text] is a random variable with density function satisfying the heat equation. In this paper, we consider...

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Autores principales: Liu, Junliang, Gao, Xiaoshan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10137932/
https://www.ncbi.nlm.nih.gov/pubmed/37190344
http://dx.doi.org/10.3390/e25040558
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author Liu, Junliang
Gao, Xiaoshan
author_facet Liu, Junliang
Gao, Xiaoshan
author_sort Liu, Junliang
collection PubMed
description Recently, Ledoux, Nair, and Wang proved that the Fisher information along the heat flow is log-convex in dimension one, that is [Formula: see text] for [Formula: see text] , where [Formula: see text] is a random variable with density function satisfying the heat equation. In this paper, we consider the high dimensional case and prove that the Fisher information is square root convex in dimension two, that is [Formula: see text] for [Formula: see text]. The proof is based on the semidefinite programming approach.
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spelling pubmed-101379322023-04-28 Square Root Convexity of Fisher Information along Heat Flow in Dimension Two Liu, Junliang Gao, Xiaoshan Entropy (Basel) Article Recently, Ledoux, Nair, and Wang proved that the Fisher information along the heat flow is log-convex in dimension one, that is [Formula: see text] for [Formula: see text] , where [Formula: see text] is a random variable with density function satisfying the heat equation. In this paper, we consider the high dimensional case and prove that the Fisher information is square root convex in dimension two, that is [Formula: see text] for [Formula: see text]. The proof is based on the semidefinite programming approach. MDPI 2023-03-24 /pmc/articles/PMC10137932/ /pubmed/37190344 http://dx.doi.org/10.3390/e25040558 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Liu, Junliang
Gao, Xiaoshan
Square Root Convexity of Fisher Information along Heat Flow in Dimension Two
title Square Root Convexity of Fisher Information along Heat Flow in Dimension Two
title_full Square Root Convexity of Fisher Information along Heat Flow in Dimension Two
title_fullStr Square Root Convexity of Fisher Information along Heat Flow in Dimension Two
title_full_unstemmed Square Root Convexity of Fisher Information along Heat Flow in Dimension Two
title_short Square Root Convexity of Fisher Information along Heat Flow in Dimension Two
title_sort square root convexity of fisher information along heat flow in dimension two
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10137932/
https://www.ncbi.nlm.nih.gov/pubmed/37190344
http://dx.doi.org/10.3390/e25040558
work_keys_str_mv AT liujunliang squarerootconvexityoffisherinformationalongheatflowindimensiontwo
AT gaoxiaoshan squarerootconvexityoffisherinformationalongheatflowindimensiontwo

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