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October 2001 A Zero-One Law for Planar Random walks in Random Environment
Franz Merkl, Martin P. W. Zerner
Ann. Probab. 29(4): 1716-1732 (October 2001). DOI: 10.1214/aop/1015345769


We solve the problem posed by S.A. Kalikow whether the event that the $x$-coordinate of a random walk in a two-dimensional random environment approaches $\infty$ has necessarily probability either zero or one. The answer is yes if we assume the environment to be i.i.d.and in general no if we allow the environment to be just stationary and ergodic.


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Franz Merkl. Martin P. W. Zerner. "A Zero-One Law for Planar Random walks in Random Environment." Ann. Probab. 29 (4) 1716 - 1732, October 2001.


Published: October 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1016.60093
MathSciNet: MR1880239
Digital Object Identifier: 10.1214/aop/1015345769

Primary: 60K37
Secondary: 60F20

Keywords: Random walk in random environment , RWRE , Zero-one law

Rights: Copyright © 2001 Institute of Mathematical Statistics

Vol.29 • No. 4 • October 2001
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