Functional inequalities for Gaussian convolutions of compactly supported measures: explicit bounds and dimension dependence
Probability
2015-07-10 v1 Functional Analysis
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 Rd. We especially focus on getting good dependence of the constants on the dimension. We prove that the Poincar{\'e} 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.
Keywords
Cite
@article{arxiv.1507.02389,
title = {Functional inequalities for Gaussian convolutions of compactly supported measures: explicit bounds and dimension dependence},
author = {Jean-Baptiste Bardet and Nathaël Gozlan and Florent Malrieu and Pierre-André Zitt},
journal= {arXiv preprint arXiv:1507.02389},
year = {2015}
}