Quenched invariance principle for random walks in balanced random environment

Details Quenched invariance principle for random walks in balanced random environment Quenched invariance principle for random walks in balanced random environment

2010-03-17

arxiv.org/abs/1003.3494v4

Mathematics

Probability

Published online in Probab. Theory Relat. Fields, 05 Oct 2010. Typo (in journal version) corrected in (26)

Scientific paper

10.1007/s00440-010-0320-9

We consider random walks in a balanced random environment in $\mathbb{Z}^d$, $d\geq 2$. We first prove an invariance principle (for $d\ge2$) and the transience of the random walks when $d\ge 3$ (recurrence when $d=2$) in an ergodic environment which is not uniformly elliptic but satisfies certain moment condition. Then, using percolation arguments, we show that under mere ellipticity, the above results hold for random walks in i.i.d. balanced environments.

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