• Bernoulli
  • Volume 24, Number 1 (2018), 333-353.

Functional inequalities for Gaussian convolutions of compactly supported measures: Explicit bounds and dimension dependence

Jean-Baptiste Bardet, Nathaël Gozlan, Florent Malrieu, and Pierre-André Zitt

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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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Bernoulli Volume 24, Number 1 (2018), 333-353.

Received: September 2015
Revised: June 2016
First available in Project Euclid: 27 July 2017

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logarithmic Sobolev inequality Poincaré inequality transport-entropy inequality


Bardet, Jean-Baptiste; Gozlan, Nathaël; Malrieu, Florent; Zitt, Pierre-André. Functional inequalities for Gaussian convolutions of compactly supported measures: Explicit bounds and dimension dependence. Bernoulli 24 (2018), no. 1, 333--353. doi:10.3150/16-BEJ879.

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