A quantitative central limit theorem for the random walk among random conductances

被引：13

作者：

Mourrat, Jean-Christophe ^{[1
]}

机构：

[1] Ecole Polytech Fed Lausanne, CH-1015 Lausanne, Switzerland

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2012年 / 17卷

关键词：

Random walk among random conductances; central limit theorem; Berry-Esseen estimate; homogenization; QUENCHED INVARIANCE-PRINCIPLES; REVERSIBLE MARKOV-PROCESSES; DIFFUSION; HOMOGENIZATION; PERCOLATION; FUNCTIONALS; DISCRETE;

D O I：

10.1214/EJP.v17-2414

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：

We consider the random walk among random conductances on Z(d). We assume that the conductances are independent, identically distributed and uniformly bounded away from 0 and infinity. We obtain a quantitative version of the central limit theorem for this random walk, which takes the form of a Berry-Esseen estimate with speed t(-1/10) for d <= 2, and speed t(-1/5) for d >= 3, up to logarithmic corrections.

引用

页码：1 / 17

页数：17

共 34 条

[1] Invariance principle for the random conductance model [J].

Andres, S. ;

Barlow, M. T. ;

Deuschel, J. -D. ;

Hambly, B. M. .

PROBABILITY THEORY AND RELATED FIELDS, 2013, 156 (3-4) :535-580

[2]

[Anonymous], 1892, London, V34, P481, DOI [10.1080/14786449208620364, DOI 10.1080/14786449208620364]

[3]

[Anonymous], 1978, DOKL AKAD NAUK SSSR

[4] INVARIANCE PRINCIPLE FOR THE RANDOM CONDUCTANCE MODEL WITH UNBOUNDED CONDUCTANCES [J].

Barlow, M. T. ;

Deuschel, J-D. .

ANNALS OF PROBABILITY, 2010, 38 (01) :234-276

[5]

Bensoussan A., 1978, Asymptotic analysis for periodic structures

[6] Quenched invariance principle for simple random walk on percolation clusters [J].

Berger, Noam ;

Biskup, Marek .

PROBABILITY THEORY AND RELATED FIELDS, 2007, 137 (1-2) :83-120

[7] Functional CLT for random walk among bounded random conductances [J].

Biskup, Marek ;

Prescott, Timothy M. .

ELECTRONIC JOURNAL OF PROBABILITY, 2007, 12 :1323-1348

[8] TAIL ESTIMATES FOR HOMOGENIZATION THEOREMS IN RANDOM MEDIA [J].

Boivin, Daniel .

ESAIM-PROBABILITY AND STATISTICS, 2009, 13 :51-69

[9] Approximations of effective coefficients in stochastic homogenization [J].

Bourgeat, A ;

Piatnitski, A .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2004, 40 (02) :153-165

[10] Finite volume approximation of the effective diffusion matrix: The case of independent bond disorder [J].

Caputo, P ;

Ioffe, D .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2003, 39 (03) :505-525

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