A variational approach to some transport inequalities
Probability
2016-04-27 v2
Abstract
We relate transport-entropy inequalities to the study of critical points of functionals defined on the space of probability measures. This approach leads in particular to a new proof of a result by Otto and Villani [43] showing that the logarithmic Sobolev inequality implies Talagrand's transport inequality.
Cite
@article{arxiv.1508.07642,
title = {A variational approach to some transport inequalities},
author = {Joaquin Fontbona and Nathael Gozlan and Jean-Francois Jabir},
journal= {arXiv preprint arXiv:1508.07642},
year = {2016}
}