Correlation and Brascamp-Lieb inequalities for Markov semigroups

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Barthe, F.
Cordero-Erausquin, D.
Ledoux, M.
Maurey, B.
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Abstract
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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.
Keywords
Mathematics - Functional Analysis, Mathematics - Probability
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