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An effective criterion for ballistic behavior of random walks in random environment
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  • Published: April 2002

An effective criterion for ballistic behavior of random walks in random environment

  • Alain-Sol Sznitman1 

Probability Theory and Related Fields volume 122, pages 509–544 (2002)Cite this article

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Abstract

 We investigate multi-dimensional random walks in random environment. Specifically, we provide an effective criterion which can be checked by inspection of the environment in a finite box, and implies a ballistic strong law of large numbers, a central limit theorem and several large deviation controls. With the help of this criterion, we provide an example of a ballistic multi-dimensional walk which does not fulfill the criterion introduced by Kalikow in [4]. The present work complements the results of [9], where a certain condition (T) was introduced, and confirms the interest of this condition.

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Authors and Affiliations

  1. Departement Mathematik, ETH-Zentrum, CH-8092 Zürich, Switzerland. e-mail: sznitman@math.ethz.ch, , , , , , CH

    Alain-Sol Sznitman

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  1. Alain-Sol Sznitman
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Received: 5 October 2000/ Revised version: 24 May 2001 Published online: 22 February 2002

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Sznitman, AS. An effective criterion for ballistic behavior of random walks in random environment. Probab Theory Relat Fields 122, 509–544 (2002). https://doi.org/10.1007/s004400100177

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  • Issue Date: April 2002

  • DOI: https://doi.org/10.1007/s004400100177

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Keywords

  • Limit Theorem
  • Central Limit
  • Central Limit Theorem
  • Random Environment
  • Deviation Control
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