Some remarks on weighted logarithmic Sobolev inequality
Patrick Cattiaux (IMT), Arnaud Guillin, Liming Wu
TL;DR
This paper presents a simplified proof of a weighted logarithmic Sobolev inequality applicable to measures like the Cauchy type, improving previous results with optimal weights and discussing related implications.
Contribution
It provides a more straightforward proof of weighted logarithmic Sobolev inequalities with optimal weights, extending and sharpening earlier results by Bobkov-Ledoux.
Findings
Simplified proof of weighted logarithmic Sobolev inequality
Optimal weight determination for Cauchy type measures
Discussion of consequences and applications
Abstract
We give here a simple proof of weighted logarithmic Sobolev inequality, for example for Cauchy type measures, with optimal weight, sharpening results of Bobkov-Ledoux. Some consequences are also discussed.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Geometric Analysis and Curvature Flows · Numerical methods in inverse problems