Functional inequalities for heavy tailed distributions and application to isoperimetry

被引：33

作者：

Cattiaux, Patrick ^{[1
]}

Gozlan, Nathael ^{[2
]}

Guillin, Arnaud ^{[3
]}

Roberto, Cyril ^{[2
]}

机构：

[1] Univ Toulouse 3, CNRS, Inst Math Toulouse, Lab Stat & Probabilites,UMR 5219, F-31062 Toulouse 09, France

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

[3] Univ Blaise Pascal, F-63177 Aubieres, France

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2010年 / 15卷

关键词：

weighted Poincare inequalities; weighted Cheeger inequalities; Lyapunov function; weak inequalities; isoperimetric profile; PROBABILITY-MEASURES; MARKOVIAN PROCESSES; SPECTRAL GAP; CONVERGENCE; DIFFUSION; STABILITY; LYAPUNOV; RATES;

D O I：

10.1214/EJP.v15-754

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：

This paper is devoted to the study of probability measures with heavy tails. Using the Lyapunov function approach we prove that such measures satisfy different kind of functional inequalities such as weak Poincare and weak Cheeger, weighted Poincare and weighted Cheeger inequalities and their dual forms. Proofs are short and we cover very large situations. For product measures on R-n we obtain the optimal dimension dependence using the mass transportation method. Then we derive (optimal) isoperimetric inequalities. Finally we deal with spherically symmetric measures. We recover and improve many previous result.

引用

页码：346 / 385

页数：40

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