Some applications of mass transport to Gaussian-type inequalities

被引:74
作者
Cordero-Erausquin, D [1 ]
机构
[1] Univ Marne La Vallee, Equipe Analyse & Math Appliquees, F-77454 Marne La Vallee 2, France
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
收藏
页码:257 / 269
页数:13
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