Convexity and regularity properties for entropic interpolations
Analysis of PDEs
2017-11-23 v1
Abstract
In this paper we prove a convexity property of the relative entropy along entropic interpolations (solutions of the Schr\"odinger problem), and a regularity property of the entropic cost along the heat flow. Then we derive a dimensional EVI inequality and a contraction property for the entropic cost along the heat flow. As a consequence, we recover the equivalent results in the Wasserstein space, proved by Erbar, Kuwada and Sturm.
Cite
@article{arxiv.1711.08230,
title = {Convexity and regularity properties for entropic interpolations},
author = {Luigia Ripani},
journal= {arXiv preprint arXiv:1711.08230},
year = {2017}
}