You are here

An entropic interpolation proof of the HWI inequality

TitleAn entropic interpolation proof of the HWI inequality
Publication TypeJournal Article
Year of Publication2019
AuthorsGentil, I, Léonard, C, Ripani, L, Tamanini, L
JournalStochastic Processes and their Applications
KeywordsEntropic interpolations; Fisher information; Relative entropy; Schrödinger problem; Wasserstein distance

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 Schrödinger 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.


Sign in