Transport-entropy inequalities on the line
Nathael Gozlan
TL;DR
This paper characterizes transport-entropy inequalities in one dimension and provides a new example of a distribution satisfying Talagrand's T2 inequality without the logarithmic Sobolev inequality.
Contribution
It offers a necessary and sufficient condition for transport-entropy inequalities in one dimension and constructs a novel distribution example.
Findings
Characterization of transport-entropy inequalities in dimension one
Construction of a distribution satisfying Talagrand's T2 but not the logarithmic Sobolev inequality
New insights into the relationship between different functional inequalities
Abstract
We give a necessary and sufficient condition for transport-entropy inequalities in dimension one. As an application, we construct a new example of a probability distribution verifying Talagrand's T2 inequality and not the logarithmic Sobolev inequality.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Point processes and geometric inequalities