Limiting velocity of high-dimensional random walk in random environment

Details Limiting velocity of high-dimensional random walk in random environment Limiting velocity of high-dimensional random walk in random environment

2006-01-26

arxiv.org/abs/math/0601656v4

Annals of Probability 2008, Vol. 36, No. 2, 728-738

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AOP338 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/07-AOP338

We show that random walk in uniformly elliptic i.i.d. environment in
dimension $\geq5$ has at most one non zero limiting velocity. In particular
this proves a law of large numbers in the distributionally symmetric case and
establishes connections between different conjectures.

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