INTERTWININGS AND GENERALIZED BRASCAMP-LIEB INEQUALITIES

Marc Arnaudon (1) , Michel Bonnefont (1) , Aldéric Joulin (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: Intertwining; Diffusion operator on vector fields; Spectral gap; Brascamp-Lieb type inequalities; Log-concave probability measure

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Marc Arnaudon, Michel Bonnefont, Aldéric Joulin. INTERTWININGS AND GENERALIZED BRASCAMP-LIEB INEQUALITIES. Revista Matemática Iberoamericana, 2018, 34. ⟨hal-01272885⟩