Intertwinings and Generalized Brascamp-Lieb Inequalities

TL;DR

This paper extends intertwining relations for Markov semigroups to multi-dimensional diffusions, deriving new Brascamp-Lieb type inequalities for log-concave distributions and illustrating them with various examples.

Contribution

It introduces generalized intertwining relations for multi-dimensional diffusions, leading to novel functional inequalities of Brascamp-Lieb type for broader classes of distributions.

Findings

Derived new functional inequalities for log-concave distributions.

Extended intertwining relations to multi-dimensional diffusions.

Provided classical and novel examples illustrating the results.

Abstract

We continue our investigation of the intertwining relations for Markov semigroups and extend the results of [9] to multi-dimensional diffusions. In particular these formulae entail new functional inequalities of Brascamp-Lieb type for log-concave distributions and beyond. Our results are illustrated by some classical and less classical examples.