A non-ballistic law of large numbers for random walks in I.I.D. Random environment

Abstract

We prove that random walks in i.i.d. random environments which oscillate in a given direction have velocity zero with respect to that direction. This complements existing results thus giving a general law of large numbers under the only assumption of a certain zero-one law, which is known to hold if the dimension is two. © 2002 Association for Symbolic Logic.