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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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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DOI: https://doi.org/10.1007/s004400100177
Keywords
- Limit Theorem
- Central Limit
- Central Limit Theorem
- Random Environment
- Deviation Control