Characterization of Talagrand's Like Transportation-Cost Inequalities on the Real Line
Nathael Gozlan (MODAL'X)
TL;DR
This paper establishes necessary and sufficient conditions for Talagrand-like transportation inequalities on the real line, expanding the class of measures with dimension-free concentration and characterizing modified Log-Sobolev inequalities for Log-concave measures.
Contribution
It provides a comprehensive characterization of transportation inequalities on the real line and introduces new examples of measures with strong concentration properties.
Findings
Identifies conditions for Talagrand-like inequalities on the real line
Expands the class of measures with dimension-free concentration
Characterizes modified Log-Sobolev inequalities for Log-concave measures
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.
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Taxonomy
TopicsPoint processes and geometric inequalities · Geometric Analysis and Curvature Flows · Mathematical Inequalities and Applications