zbMATH — the first resource for mathematics

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.

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