An effective criterion for ballistic behavior of random walks in random environment (Q1606049)

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 \textit{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.