Open Access
November 2008 Transient random walks on a strip in a random environment
Alexander Roitershtein
Ann. Probab. 36(6): 2354-2387 (November 2008). DOI: 10.1214/08-AOP393


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.


Download Citation

Alexander Roitershtein. "Transient random walks on a strip in a random environment." Ann. Probab. 36 (6) 2354 - 2387, November 2008.


Published: November 2008
First available in Project Euclid: 19 December 2008

zbMATH: 1167.60023
MathSciNet: MR2478686
Digital Object Identifier: 10.1214/08-AOP393

Primary: 60K37
Secondary: 60F05 , 60F10

Keywords: central limit theorem , environment viewed from the particle , hitting times , random environment , random walks on a strip , Renewal structure , Strong law of large numbers

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 6 • November 2008
Back to Top