Electronic Communications in Probability

A Non-Ballistic Law of Large Numbers for Random Walks in I.I.D. Random Environment

Martin Zerner

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We prove that random walks in i.i.d. random environments which oscillate in a given direction have velocity zero with respect to that direction. This complements existing results thus giving a general law of large numbers under the only assumption of a certain zero-one law, which is known to hold if the dimension is two.

Article information

Electron. Commun. Probab., Volume 7 (2002), paper no. 19, 191-197.

Accepted: 30 September 2002
First available in Project Euclid: 16 May 2016

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments
Secondary: 60F15: Strong theorems

Random walk in random environment RWRE law of large numbers

This work is licensed under aCreative Commons Attribution 3.0 License.


Zerner, Martin. A Non-Ballistic Law of Large Numbers for Random Walks in I.I.D. Random Environment. Electron. Commun. Probab. 7 (2002), paper no. 19, 191--197. doi:10.1214/ECP.v7-1060. https://projecteuclid.org/euclid.ecp/1463434786

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