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On stochastic domination in the Brascamp–Lieb framework

Published online by Cambridge University Press:  02 May 2003

GIAMBATTISTA GIACOMIN
Affiliation:
Université Paris 7 – Denis Diderot, U.F.R. Mathematiques and Laboratoire de Probabilités et Modèles Aléatoires, CNRS U.M.R. 7599 Case 7012, 2 place Jussieu, 75251 Paris cedex 05, France. e-mail: [email protected]

Abstract

We exploit a recent approach to Brascamp–Lieb inequalities, due to Caffarelli [5], 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 Prékopa and Leindler and they complement the Brascamp–Lieb moment inequalities. Some applications to a class of Gibbs measures, the anharmonic crystals, are developed.

Type
Research Article
Copyright
2003 Cambridge Philosophical Society

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