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

• François Bolley ^[1] ; Ivan Gentil ^[2] ; Arnaud Guillin ^[3]
  1. [1] Pierre and Marie Curie University

     Pierre and Marie Curie University

     París, Francia

     
  2. [2] University of Lyon System

     University of Lyon System

     Arrondissement de Lyon, Francia

     
  3. [3] University of Clermont Auvergne

     University of Clermont Auvergne

     Arrondissement de Clermont-Ferrand, Francia

     

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 46, Nº. 1, 2018, págs. 261-301
• Idioma: inglés
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  • 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 behavior for the laws of solutions to stochastic differential equations.