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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Detalles Bibliográficos
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
Descripción
Sumario: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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