An entropic interpolation proof of the HWI inequality

Ivan Gentil; Christian Léonard; Luigia Ripani; Luca Tamanini

doi:10.1016/j.spa.2019.04.002

An entropic interpolation proof of the HWI inequality

Ivan Gentil^*
, Christian Léonard
, Luigia Ripani
, Luca Tamanini

^*Corresponding author

Universite Claude Bernard Lyon 1
Université Paris Nanterre

Research output: Contribution to journal › Article

Abstract

The HWI inequality is an "interpolation" inequality between the Entropy H, the Fisher information I and the Wasserstein distance W. We present a pathwise proof of the HWI inequality which is obtained through a zero noise limit of the Schrodinger problem. Our approach consists in making rigorous the Otto-Villani heuristics in Otto and Villani (2000) taking advantage of the entropic interpolations, which are regular both in space and time, rather than the displacement ones.

Original language	English
Pages (from-to)	907-923
Number of pages	17
Journal	Stochastic Processes and their Applications
Volume	130
DOIs	https://doi.org/10.1016/j.spa.2019.04.002
Publication status	Published - 2020

Keywords

Entropic interpolations
Fisher information
Relative entropy
Schrodinger problem
Wasserstein distance

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10.1016/j.spa.2019.04.002

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T1 - An entropic interpolation proof of the HWI inequality

AU - Gentil, Ivan

AU - Léonard, Christian

AU - Ripani, Luigia

AU - Tamanini, Luca

PY - 2020

Y1 - 2020

N2 - The HWI inequality is an "interpolation" inequality between the Entropy H, the Fisher information I and the Wasserstein distance W. We present a pathwise proof of the HWI inequality which is obtained through a zero noise limit of the Schrodinger problem. Our approach consists in making rigorous the Otto-Villani heuristics in Otto and Villani (2000) taking advantage of the entropic interpolations, which are regular both in space and time, rather than the displacement ones.

AB - The HWI inequality is an "interpolation" inequality between the Entropy H, the Fisher information I and the Wasserstein distance W. We present a pathwise proof of the HWI inequality which is obtained through a zero noise limit of the Schrodinger problem. Our approach consists in making rigorous the Otto-Villani heuristics in Otto and Villani (2000) taking advantage of the entropic interpolations, which are regular both in space and time, rather than the displacement ones.

KW - Entropic interpolations

KW - Fisher information

KW - Relative entropy

KW - Schrodinger problem

KW - Wasserstein distance

KW - Entropic interpolations

KW - Fisher information

KW - Relative entropy

KW - Schrodinger problem

KW - Wasserstein distance

UR - http://hdl.handle.net/10807/232496

U2 - 10.1016/j.spa.2019.04.002

DO - 10.1016/j.spa.2019.04.002

M3 - Article

SN - 0304-4149

VL - 130

SP - 907

EP - 923

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

ER -

An entropic interpolation proof of the HWI inequality

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Keywords

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