Correlation and Brascamp–Lieb Inequalities for Markov Semigroups

By Franck Barthe, Dario Cordero-Erausquin, Michel Ledoux, B. Maurey. 2009

49 citations recorded by the source corpus.

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 two-fold. 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. Related superadditivity of information and entropy inequalities are also studied.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/87a70415b16c9d8eec436a62a47a041609a24045

Citations in the corpus

• Monotonicity and its analytic and geometric implications (2012, unknown): “M Hesslog u þ 1 2t g 2 þRicð∇ log u;∇ loguÞ u; [3]”