Modified logarithmic Sobolev inequalities and transportation inequalities |
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| Authors: | Email author" target="_blank">Ivan?GentilEmail author Arnaud?Guillin Laurent?Miclo |
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| Institution: | (1) Ceremade (UMR CNRS no. 7534), Université Paris-Dauphine, Place du Maréchal De Lattre De Tassigny, Paris, Cédex 16, 75775, France;(2) Laboratoire d'Analyse, Topologie, Probabilités (UMR CNRS no. 6632), Université de Provence, 39, rue F. Joliot Curie, Marseille, cédex 13, 13453, France |
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| Abstract: | We present a class of modified logarithmic Sobolev inequality, interpolating between Poincaré and logarithmic Sobolev inequalities,
suitable for measures of the type exp (−|x|α) or exp (−|x|α log β(2+|x|)) (α ∈]1,2 and β ∈ ℝ) 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.
Send offprint requests to: Ivan Gentil |
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