Characterization of Talagrand’s like transportation-cost inequalities on the real line

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. © 2007 Elsevier Inc. All rights reserved