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Characterization of Talagrand's Like Transportation-Cost Inequalities on the Real Line

Nathael Gozlan
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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 R.

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Nathael Gozlan. 2006-08-10. Characterization of Talagrand's Like Transportation-Cost Inequalities on the Real Line. https://arxiv.org/abs/math/0608241

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