An entropic interpolation proof of the HWI inequality

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

*Autore corrispondente per questo lavoro

Risultato della ricerca: Contributo in rivistaArticolo in rivista

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.
Lingua originaleEnglish
pagine (da-a)907-923
Numero di pagine17
RivistaStochastic Processes and their Applications
Volume130
DOI
Stato di pubblicazionePubblicato - 2020

Keywords

  • Entropic interpolations
  • Fisher information
  • Relative entropy
  • Schrodinger problem
  • Wasserstein distance

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