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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Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2018, 24 (1), pp.333-353. 〈10.3150/16-BEJ879〉
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Dernière modification le : jeudi 7 décembre 2017 - 12:34:03
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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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