Correlation and Brascamp-Lieb inequalities for Markov semigroups
Functional Analysis
2009-07-17 v1 Probability
Abstract
This paper builds upon several recent works, where semigroup proofs of Brascamp-Lieb inequalities are provided in various settings (Euclidean space, spheres and symmetric groups). Our aim is twofold. Firstly, we provide a general, unifying, framework based on Markov generators, in order to cover a variety of examples of interest going beyond previous investigations. Secondly, we put forward the combinatorial reasons for which unexpected exponents occur in these inequalities.
Cite
@article{arxiv.0907.2858,
title = {Correlation and Brascamp-Lieb inequalities for Markov semigroups},
author = {F. Barthe and D. Cordero-Erausquin and M. Ledoux and B. Maurey},
journal= {arXiv preprint arXiv:0907.2858},
year = {2009}
}