Quenched Limit Theorems for Nearest Neighbour Random Walks in 1D Random Environment

被引：26

作者：

Dolgopyat, D. ^{[1
,2
]}

Goldsheid, I. ^{[3
]}

机构：

[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[2] Univ Maryland, Inst Phys Sci & Technol, College Pk, MD 20742 USA

[3] Queen Mary Univ London, Sch Math Sci, London E1 4NS, England

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2012年 / 315卷 / 01期

基金：

美国国家科学基金会;

关键词：

DIMENSIONAL RANDOM-WALK; TRANSIENT RANDOM-WALKS; RENEWAL THEORY; LAWS;

D O I：

10.1007/s00220-012-1539-3

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

It is well known that random walks in a one dimensional random environment can exhibit subdiffusive behavior due to the presence of traps. In this paper we show that the passage times of different traps are asymptotically independent exponential random variables with parameters forming, asymptotically, a Poisson process. This allows us to prove weak quenched limit theorems in the subdiffusive regime where the contribution of traps plays the dominating role.

引用

页码：241 / 277

页数：37

共 26 条

[1]

[Anonymous], 2007, EXTREME VALUES REGUL

[2] Recurrence and transience of random walks in random environments on a strip [J].

Bolthausen, E ;

Goldsheid, I .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2000, 214 (02) :429-447

[3] Anomalous current in periodic Lorentz gases with infinite horizon [J].

Dolgopyat, D. I. ;

Chernov, N. I. .

RUSSIAN MATHEMATICAL SURVEYS, 2009, 64 (04) :651-699

[4]

ENRIQUEZ N., 2010, STABLE FLUCTUATIONS

[5]

Enriquez N., FREIMANS CONJECTURE

[6] LIMIT LAWS FOR TRANSIENT RANDOM WALKS IN RANDOM ENVIRONMENT ON Z [J].

Enriquez, Nathanael ;

Sabot, Christophe ;

Zindy, Olivier .

ANNALES DE L INSTITUT FOURIER, 2009, 59 (06) :2469-2508

[7] AGING AND QUENCHED LOCALIZATION FOR ONE-DIMENSIONAL RANDOM WALKS IN RANDOM ENVIRONMENT IN THE SUB-BALLISTIC REGIME [J].

Enriquez, Nathanael ;

Sabot, Christophe ;

Zindy, Olivier .

BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 2009, 137 (03) :423-452

[8] Many visits to a single site by a transient random walk in random environment [J].

Gantert, N ;

Shi, Z .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2002, 99 (02) :159-176

[9] Linear and sub-linear growth and the CLT for hitting times of a random walk in random environment on a strip [J].

Goldsheid, Ilya Ya. .

PROBABILITY THEORY AND RELATED FIELDS, 2008, 141 (3-4) :471-511

[10] Simple transient random walks in one-dimensional random environment: the central limit theorem [J].

Goldsheid, Ilya Ya. .

PROBABILITY THEORY AND RELATED FIELDS, 2007, 139 (1-2) :41-64

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