The zero-one lawfor planar randomwalks in I.I.D. random environments revisited

Abstract

In this note we present a simplified proof of the zero-one law by Merkl and Zerner (2001) for directional transience of random walks in i.i.d. random environments (RWRE) on ℤ2. Also, we indicate how to construct a two-dimensional counterexample in a non-uniformly elliptic and stationary environment which has better ergodic properties than the example given by Merkl and Zerner. © 2007 Applied Probability Trust.