Correlation and Brascamp-Lieb inequalities for Markov semigroups

2009/07/16 by F. Barthe, Dario Cordero–Erausquin, Barthe, F. +7 · 4 citations
Computer Science · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Topological and Geometric Data Analysis #math.FA #math.PR

paper · pdf · doi:10.48550/arxiv.0907.2858

arxiv created 2009/07/16 · openalex publication_date 2009/07/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Logarithmic Sobolev inequalities for finite Markov chains

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