Calculus of Variations and Geometric Measure Theory

I. Gentil - C. LĂ©onard - L. Ripani - L. Tamanini

An entropic interpolation proof of the HWI inequality

created by tamanini1 on 04 Jun 2018
modified on 16 Jul 2019


Published Paper

Inserted: 4 jun 2018
Last Updated: 16 jul 2019

Journal: Stochastic Process. Appl.
Year: 2018


We present a pathwise proof of the HWI inequality which is based on entropic interpolations rather than displacement ones. Unlike the latter, entropic interpolations are regular both in space and time. Consequently, our approach is closer to the Otto-Villani heuristics, presented in the first part of the article $[23]$, than the original rigorous proof presented in the second part of $[23]$.