Free Functional Inequalities on the Circle
Probability
2017-10-24 v3
Abstract
In this paper we deal with free functional inequalities on the circle. There are some interesting changes as opposed to the classical case. For example, the free Poincar\'e inequality has a slight change which seems to account for the lack of invariance under rotations of the base measure. Another instance is the modified Wasserstein distance on the circle which provides the tools for analyzing transportation, Log-Sobolev, and HWI inequalities. These new phenomena also indicate that they have a classical counterpart, which does not seem to have been investigated before.
Keywords
Cite
@article{arxiv.1511.05274,
title = {Free Functional Inequalities on the Circle},
author = {Ionel Popescu},
journal= {arXiv preprint arXiv:1511.05274},
year = {2017}
}
Comments
It will appear in Advances of Mathematics