Bounds on the deficit in the logarithmic Sobolev inequality

被引：43

作者：

Bobkov, S. G. ^{[1
]}

Gozlan, N. ^{[2
]}

Roberto, C. ^{[3
]}

Samson, P. -M. ^{[2
]}

机构：

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[2] Univ Paris Est Marne La Vallee, Lab Anal & Math Appliquees, UMR CNRS 8050, F-77454 Marne La Vallee 2, France

[3] Univ Paris Quest Nanterre Def, MODALX, EA 3454, F-92000 Nanterre, France

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2014年 / 267卷 / 11期

基金：

美国国家科学基金会;

关键词：

Logarithmic Sobolev inequality; Probability distances; Optimal transport; Gaussian measures; TRANSPORTATION-COST; MASS-TRANSPORT; INFORMATION; PROOF; HYPERCONTRACTIVITY; STABILITY;

D O I：

10.1016/j.jfa.2014.09.016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The deficit in the logarithmic Sobolev inequality for the Gaussian measure is considered and estimated by means of transport and information-theoretic distances. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：4110 / 4138

页数：29

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[1]

Ane C., 2000, INEGALITES SOBOLEV L, V10

[2]

Bakry D., 1985, SEM PROB 19, V1123, P177

[3]

Bakry D, 2006, REV MAT IBEROAM, V22, P683

[4] Dimension dependent hypercontractivity for Gaussian kernels [J].