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

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 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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https://hal.archives-ouvertes.fr/hal-01172549
Contributor : Pierre-André Zitt <>
Submitted on : Wednesday, July 8, 2015 - 9:03:57 AM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM
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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, Bernoulli Society for Mathematical Statistics and Probability, 2018, 24 (1), pp.333-353. ⟨10.3150/16-BEJ879⟩. ⟨hal-01172549⟩

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