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Article Dans Une Revue Bernoulli Année : 2018

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

Résumé

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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Dates et versions

hal-01172549 , version 1 (08-07-2015)

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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, 2018, 24 (1), pp.333-353. ⟨10.3150/16-BEJ879⟩. ⟨hal-01172549⟩
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