CONVEX CONCENTRATION INEQUALITIES FOR CONTINUOUS GAS AND STOCHASTIC DOMINATION

被引：2

作者：

Ma Yutao ^{[1
,2
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[2] Beijing Normal Univ, Lab Math & Complex Syst, Beijing 100875, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2009年 / 29卷 / 05期

关键词：

continuous gas; Gibbs measure; convex concentration inequality; Ito's formula; stochastic domination; SPECTRAL GAP;

D O I：

10.1016/S0252-9602(09)60118-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we consider the continuous gas in a bounded domain A of R+ or R-d described by a Gibbsian probability measure mu(eta)(Lambda) associated with a pair interaction phi, the inverse temperature beta, the activity z > 0, and the boundary condition eta. Define F = integral f(s)omega(Lambda) (ds). Applying the generalized Ito's formula for forward-backward martingales (see Klein et al. [5]), we obtain convex concentration inequalities for F with respect to the Gibbs measure mu(eta)(Lambda). On the other hand, by FKG inequality on the Poisson space, we also give a new simple argument for the stochastic domination for the Gibbs measure.

引用

页码：1461 / 1468

页数：8