Electronic Communications in Probability

Electronic Communications in Probability > Vol. 12 (2007) > Paper 32

The zero-one law for planar random walks in i.i.d. random environments revisited

Martin P.W. Zerner, University of Tuebingen

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 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.

Full text: PDF

Pages: 326-335

Published on: October 5, 2007

Bibliography

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Electronic Communications in Probability. ISSN: 1083-589X