Characterization of Talagrand's like transportation-cost inequalities on the real line |
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| Authors: | Nathael Gozlan |
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| Affiliation: | aLaboratoire d'Analyse et de Mathématiques Appliquées, UMR CNRS 8050, Université Paris-Est, 5 bd Descartes, 77454 Marne la Vallée Cedex 2, France |
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| Abstract: | In this paper, we give necessary and sufficient conditions for Talagrand's like transportation cost inequalities on the real line. This brings a new wide class of examples of probability measures enjoying a dimension-free concentration of measure property. Another byproduct is the characterization of modified Log-Sobolev inequalities for log-concave probability measures on  . |
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| Keywords: | Transportation cost inequalities Concentration of measure Logarithmic Sobolev inequalities |
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