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Recurrence and Transience of Random Walks¶in Random Environments on a Strip

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Abstract:

We explain the necessary and sufficient conditions for recurrent and transient behavior of a random walk in a stationary ergodic random environment on a strip in terms of properties of a top Lyapunov exponent. This Lyapunov exponent is defined for a product of a stationary sequence of positive matrices. In the one-dimensional case this approach allows us to treat wider classes of random walks than before.

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Authors and Affiliations

  1. Universität Zürich, Institut für Mathematik, Winterthurerstrasse 190, 8057 Zürich, Switzerland, , , , , , CH

    Erwin Bolthausen

  2. School of Mathematical Sciences, Queen Mary and Westfield College, University of London,¶London E1 4NS, UK, , , , , , GB

    Ilya Goldsheid

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  1. Erwin Bolthausen
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  2. Ilya Goldsheid
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Received: 15 March 2000 / Accepted: 14 April 2000

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Bolthausen, E., Goldsheid, I. Recurrence and Transience of Random Walks¶in Random Environments on a Strip. Commun. Math. Phys. 214, 429–447 (2000). https://doi.org/10.1007/s002200000279

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  • DOI: https://doi.org/10.1007/s002200000279

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