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

 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.