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. 
Nathael Gozlan (MODAL'X)