Annals of Probability

Transient random walks on a strip in a random environment

Alexander Roitershtein

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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

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

First available in Project Euclid: 19 December 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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