A Glivenko-Cantelli theorem for almost additive functions on lattices

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Schumacher, Christoph¹  Schwarzenberger, Fabian^1,2  Veselic, Ivan¹ 

[1] Tech Univ Chemnitz, Fak Math, D-09107 Chemnitz, Germany

[2] Hsch Tech & Wirtschaft Dresden, Fak Informat Math, D-01069 Dresden, Germany

关键词: Glivenko-Cantelli theory;    Uniform convergence;    Empirical measures;    Large deviations;    Statistical mechanics;   

DOI  :  10.1016/j.spa.2016.06.005

来源: Elsevier

【 摘 要 】

We develop a Glivenko-Cantelli theory for monotone, almost additive functions of i.i.d. sequences of random variables indexed by Z(d). Under certain conditions on the random sequence, short range correlations are allowed as well. We have an explicit error estimate, consisting of a probabilistic and a geometric part. We apply the results to yield uniform convergence for several quantities arising naturally in statistical physics. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free