Symmetrized Talagrand Inequalities on Euclidean Spaces
Hiroshi Tsuji

TL;DR
This paper explores symmetrized Talagrand inequalities in Euclidean spaces, providing new proofs, refined functional inequalities, and applications related to convex geometry and probability.
Contribution
It offers an alternative proof of Fathi's inequality, extends the inequality to Euclidean spaces, and derives refined functional inequalities and applications.
Findings
Alternative proof of Fathi's symmetrized Talagrand inequality on the real line
Refined functional inequalities under specific conditions
Connections established with convex geometry and applications
Abstract
In this paper, we study the symmetrized Talagrand inequality that was proved by Fathi and has a connection with the Blaschke-Santal\'{o} inequality in convex geometry. As corollaries of our results, we have several refined functional inequalities under some conditions. We also give an alternative proof of Fathi's symmetrized Talagrand inequality on the real line and some applications.
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Taxonomy
TopicsMathematical Inequalities and Applications · Point processes and geometric inequalities · Geometric Analysis and Curvature Flows
