Asymptotic direction in random walks in random environment revisited

Alexander Drewitz, Alejandro F. Ramírez
2010 Brazilian Journal of Probability and Statistics  
Recently Simenhaus in [Sim07] proved that for any elliptic random walk in random environment, transience in the neighborhood of a given direction is equivalent to the a.s. existence of a deterministic asymptotic direction and to transience in any direction in the open half space defined by this asymptotic direction. Here we prove an improved version of this result and review some open problems.
doi:10.1214/09-bjps028 fatcat:4q6bbq47pza6xivz3vgedtriba