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 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.Comment: 9 page
