Optimal Concentration Inequalities for Dynamical Systems

被引：30

作者：

Chazottes, Jean-Rene ^{[1
]}

Gouezel, Sebastien ^{[2
]}

机构：

[1] Ecole Polytech, CNRS, CPHT, UMR 7644, F-91128 Palaiseau, France

[2] Univ Rennes 1, IRMAR, CNRS, UMR 6625, F-35042 Rennes, France

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2012年 / 316卷 / 03期

关键词：

DEVROYE INEQUALITY; RANDOM-VARIABLES; MIXING RATES; MAPS; DECAY; BILLIARDS; INTERVAL; MOMENT;

D O I：

10.1007/s00220-012-1596-7

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

For dynamical systems modeled by a Young tower with exponential tails, we prove an exponential concentration inequality for all separately Lipschitz observables of n variables. When tails are polynomial, we prove polynomial concentration inequalities. Those inequalities are optimal. We give some applications of such inequalities to specific systems and specific observables.

引用

页码：843 / 889

页数：47

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