Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### On stochastic domination in the Brascamp--Lieb framework

Auteur(s):

Code(s) de Classification MSC:

• 26D15 Inequalities for sums, series and integrals
• 82B20 Lattice systems (Ising, dimer, Potts, etc.)

Résumé: We exploit a recent approach to Brascamp-Lieb inequalities, due to L. Caffarelli, and reconsider earlier approaches to establish stochastic domination inequalities between Gaussian variables and random variables with density of the form $g\cdot h$, $g$ a Gaussian density and $h$ a log--concave or log--convex function. These extend to inequalities on random vectors via a classical result by A.~Pr\'ekopa and L.~Leindler %\cite[Theorem~4.3]{cf:BL} and they complement the Brascamp--Lieb moment inequalities. Some applications to a class of Gibbs measures, the {\sl anharmonic crystals}, are developed.

Mots Clés: Log-concave distributions ; Stochastic domination ; Log-convexity ; Brascamp-Lieb inequalities ; Optimal mass transportation ; Anharmonic crystal

Date: 2002-07-10

Prépublication numéro: PMA-751

Pdf file : PMA-751.pdf