DIMENSIONAL IMPROVEMENTS OF THE LOGARITHMIC SOBOLEV, TALAGRAND AND BRASCAMP-LIEB INEQUALITIES

被引：21

作者：

Bolley, Francois ^{[1
]}

Gentil, Ivan ^{[2
]}

Guillin, Arnaud ^{[3
]}

机构：

[1] Univ Paris 06, CNRS, Lab Probabil & Modeles Aleatoires, UMR 7599, 4 Pl Jussieu, F-75005 Paris, France

[2] Univ Claude Bernard Lyon 1, Univ Lyon, Inst Camille Jordan, UMR 5208,CNRS, 43 Blvd 11 Novembre 1918, F-69622 Villeurbanne, France

[3] Univ Clermont Auvergne, CNRS, Lab Math, UMR 6620, Ave Landais, F-63177 Aubiere, France

来源：

ANNALS OF PROBABILITY | 2018年 / 46卷 / 01期

关键词：

Logarithmic Sobolev inequality; Talagrand inequality; Brascamp-Lieb inequality; Fokker-Planck equations; optimal transport; HAMILTON-JACOBI EQUATIONS; BRUNN-MINKOWSKI; GRADIENT FLOWS; MASS-TRANSPORT; HYPERCONTRACTIVITY; DISTANCE; SPACES;

D O I：

10.1214/17-AOP1184

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this work, we consider dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities. For this, we use optimal transport methods and the Borell-Brascamp-Lieb inequality. These refinements can be written as a deficit in the classical inequalities. They have the right scale with respect to the dimension. They lead to sharpened concentration properties as well as refined contraction bounds, convergence to equilibrium and short time behavior for the laws of solutions to stochastic differential equations.

引用

页码：261 / 301

页数：41

共 39 条

[1]

Ambrosio L., 2008, LECT MATH ETH ZURICH

[2]

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

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