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February 2018 Functional inequalities for Gaussian convolutions of compactly supported measures: Explicit bounds and dimension dependence
Jean-Baptiste Bardet, Nathaël Gozlan, Florent Malrieu, Pierre-André Zitt
Bernoulli 24(1): 333-353 (February 2018). DOI: 10.3150/16-BEJ879

Abstract

The aim of this paper is to establish various functional inequalities for the convolution of a compactly supported measure and a standard Gaussian distribution on $\mathbb{R}^{d}$. We especially focus on getting good dependence of the constants on the dimension. We prove that the Poincaré inequality holds with a dimension-free bound. For the logarithmic Sobolev inequality, we improve the best known results (Zimmermann, JFA 2013) by getting a bound that grows linearly with the dimension. We also establish transport-entropy inequalities for various transport costs.

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Jean-Baptiste Bardet. Nathaël Gozlan. Florent Malrieu. Pierre-André Zitt. "Functional inequalities for Gaussian convolutions of compactly supported measures: Explicit bounds and dimension dependence." Bernoulli 24 (1) 333 - 353, February 2018. https://doi.org/10.3150/16-BEJ879

Information

Received: 1 September 2015; Revised: 1 June 2016; Published: February 2018
First available in Project Euclid: 27 July 2017

zbMATH: 06778331
MathSciNet: MR3706760
Digital Object Identifier: 10.3150/16-BEJ879

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

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Vol.24 • No. 1 • February 2018
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