AN ENTROPIC INTERPOLATION PROOF OF THE HWI INEQUALITY

Ivan Gentil (1) , Christian Léonard (2) , Luigia Ripani (1) , Luca Tamanini (3)

1 ICJ - Institut Camille Jordan
2 MODAL'X - Modélisation aléatoire de Paris X
3 Institut für Angewandte Mathematik

We present a pathwise proof of the HWI inequality which is based on en-tropic 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].

Domaines: Probabilités [math.PR]; Analyse classique [math.CA]

Ivan Gentil, Christian Léonard, Luigia Ripani, Luca Tamanini. AN ENTROPIC INTERPOLATION PROOF OF THE HWI INEQUALITY. 2018. ⟨hal-01840629v1⟩