2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129905In 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 the square lattice. 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.9 pagesProbabilityPrimary 60K37, secondary 60F20.text