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

2006/08/10 by Nathaël Gozlan, Gozlan, Nathael · 2 citations
Mathematics · #60E15 26D10 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Inequalities and Applications #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.math/0608241

openalex publication_date 2006/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality

Cited by

• Generalized Blaschke--Santaló-type inequalities, without symmetry restrictions
• Concentration of measure for non-linear random matrices with applications to neural networks and non-commutative polynomials

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