Some applications of mass transport to Gaussian-type inequalities

被引：76

作者：

Cordero-Erausquin, D ^{[1
]}

机构：

[1] Univ Marne La Vallee, Equipe Analyse & Math Appliquees, F-77454 Marne La Vallee 2, France

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2002年 / 161卷 / 03期

关键词：

D O I：

10.1007/s002050100185

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

As discovered by Brenier, mapping through a convex gradient gives the optimal transport in R-n. In the present article, this map is used in the setting of Gaussian-like measures to derive an inequality linking entropy with mass displacement by a straightforward argument. As a consequence, logarithmic Sobolev and transport inequalities are recovered. Finally, a result of Caffarelli on the Brenier map is used to obtain Gaussian correlation inequalities.

引用

页码：257 / 269

页数：13

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