From dimension free concentration to Poincar\'e inequality
Probability
2013-10-10 v2 Functional Analysis
Abstract
We prove that a probability measure on an abstract metric space satisfies a non trivial dimension free concentration inequality for the metric if and only if it satisfies the Poincar\'e inequality.
Keywords
Cite
@article{arxiv.1305.4331,
title = {From dimension free concentration to Poincar\'e inequality},
author = {Nathael Gozlan and Cyril Roberto and Paul-Marie Samson},
journal= {arXiv preprint arXiv:1305.4331},
year = {2013}
}