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

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.

References in corpus (1)

• Transportation cost-information inequalities and applications to random dynamical systems and diffusions

Cited by in corpus (1)

• Modified log-Sobolev inequalities and isoperimetry