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January 2018 Dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp–Lieb inequalities
François Bolley, Ivan Gentil, Arnaud Guillin
Ann. Probab. 46(1): 261-301 (January 2018). DOI: 10.1214/17-AOP1184

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 behavior for the laws of solutions to stochastic differential equations.

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François Bolley. Ivan Gentil. Arnaud Guillin. "Dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp–Lieb inequalities." Ann. Probab. 46 (1) 261 - 301, January 2018. https://doi.org/10.1214/17-AOP1184

Information

Received: 1 October 2015; Revised: 1 March 2017; Published: January 2018
First available in Project Euclid: 5 February 2018

zbMATH: 06865123
MathSciNet: MR3758731
Digital Object Identifier: 10.1214/17-AOP1184

Subjects:
Primary: 60E15, 60H10, 60J60

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 1 • January 2018
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