Electronic Communications in Probability

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

Martin Zerner

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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.

Article information

Electron. Commun. Probab., Volume 12 (2007), paper no. 32, 326-335.

Accepted: 5 October 2007
First available in Project Euclid: 6 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments
Secondary: 60F20: Zero-one laws

Random environment random walk RWRE transience zero-one law

This work is licensed under aCreative Commons Attribution 3.0 License.


Zerner, Martin. The zero-one law for planar random walks in i.i.d. random environments revisited. Electron. Commun. Probab. 12 (2007), paper no. 32, 326--335. doi:10.1214/ECP.v12-1314. https://projecteuclid.org/euclid.ecp/1465224975

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