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Modified logarithmic Sobolev inequalities and transportation inequalities

Abstract : We present a new class of modified logarithmic Sobolev inequality, interpolating between Poincaré and logarithmic Sobolev inequalities, suitable for measures of the type $\exp(-|x|^\al)$ or $\exp(-|x|^\al\log^\beta(2+|x|))$ ($\al\in]1,2[$ and $\be\in\dR$) which lead to new concentration inequalities. These modified inequalities share common properties with usual logarithmic Sobolev inequalities, as tensorisation or perturbation, and imply as well Poincaré inequality. We also study the link between these new modified logarithmic Sobolev inequalities and transportation inequalities.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-00001609
Contributor : Ivan Gentil <>
Submitted on : Monday, May 24, 2004 - 4:23:23 PM
Last modification on : Wednesday, February 19, 2020 - 8:56:14 AM
Document(s) archivé(s) le : Monday, March 29, 2010 - 8:34:03 PM

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  • HAL Id : hal-00001609, version 1

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Ivan Gentil, Arnaud Guillin, Laurent Miclo. Modified logarithmic Sobolev inequalities and transportation inequalities. Probability Theory and Related Fields, Springer Verlag, 2005, 133 (3), pp.409-436. ⟨hal-00001609⟩

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