Dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities

Abstract : In this work we consider dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities. For this we use optimal transport methods and the Borell-Brascamp-Lieb inequality. These refinements can be written as a deficit in the classical inequalities. They have the right scale with respect to the dimension. They lead to sharpened concentration properties as well as refined contraction bounds, convergence to equilibrium and short time behaviour for the laws of solutions to stochastic differential equations.
Type de document :
Pré-publication, Document de travail
2015
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01171361
Contributeur : Ivan Gentil <>
Soumis le : dimanche 12 mars 2017 - 22:13:08
Dernière modification le : lundi 20 mars 2017 - 17:17:34

Fichiers

HAL4-Bolley-Gentil-Guillin--IF...
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01171361, version 4
  • ARXIV : 1507.01086

Citation

François Bolley, Ivan Gentil, Arnaud Guillin. Dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities. 2015. <hal-01171361v4>

Partager

Métriques

Consultations de
la notice

119

Téléchargements du document

11