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.
Citation
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
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