Annals of Probability

Transient random walks on a strip in a random environment

Alexander Roitershtein

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Abstract

We consider transient random walks on a strip in a random environment. The model was introduced by Bolthausen and Goldsheid [Comm. Math. Phys. 214 (2000) 429–447]. We derive a strong law of large numbers for the random walks in a general ergodic setup and obtain an annealed central limit theorem in the case of uniformly mixing environments. In addition, we prove that the law of the “environment viewed from the position of the walker” converges to a limiting distribution if the environment is an i.i.d. sequence.

Article information

Source
Ann. Probab., Volume 36, Number 6 (2008), 2354-2387.

Dates
First available in Project Euclid: 19 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.aop/1229696606

Digital Object Identifier
doi:10.1214/08-AOP393

Mathematical Reviews number (MathSciNet)
MR2478686

Zentralblatt MATH identifier
1167.60023

Subjects
Primary: 60K37: Processes in random environments
Secondary: 60F05: Central limit and other weak theorems 60F10: Large deviations

Keywords
Central limit theorem environment viewed from the particle hitting times random walks on a strip random environment renewal structure strong law of large numbers

Citation

Roitershtein, Alexander. Transient random walks on a strip in a random environment. Ann. Probab. 36 (2008), no. 6, 2354--2387. doi:10.1214/08-AOP393. https://projecteuclid.org/euclid.aop/1229696606


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