Characterization of Talagrand's like transportation-cost inequalities on the real line (Q2456990)

This article is devoted to the study of probability measures on the real axis satisfying some kind of transportation-cost inequalities. These inequalities relate two quantities: on the one hand, an optional transportation cost in the sense of Kantorovich and on the other hand, the relative entropy (also called Kullback-Leibler distance). In fact, the author gives necessary and sufficient conditions for Talagrand 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. Anothor byproduct is the characterization of modified log-Sobolev inequalities for log-concave probability measures on the real axis.