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An effective criterion for ballistic behavior of random walks in random environment. (English) Zbl 0995.60097
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 S. A. Kalikow [Ann. Stat. 9, 753-768 (1981; Zbl 0545.60065)]. The present work complements the results of the author [ibid. 29, No. 2, 724-765 (2001)], where a certain condition (T) was introduced, and confirms the interest of this condition.

MSC:
60K37 Processes in random environments
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
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