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BIASED RANDOM WALK ON DYNAMICAL PERCOLATION

Accepted version
Peer-reviewed

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Authors

Sousi, Perla 

Abstract

We study biased random walks on dynamical percolation on Zd. We es- tablish a law of large numbers and an invariance principle for the random walk using regeneration times. Moreover, we verify that the Einstein rela- tion holds, and we investigate the speed of the walk as a function of the bias. While for d = 1 the speed is increasing, we show that in general this fails in dimension d ≥ 2. As our main result, we establish two regimes of parameters, separated by an explicit critical curve, such that the speed is either eventually strictly increasing or eventually strictly decreasing. This is in sharp contrast to the biased random walk on a static supercritical percolation cluster, where the speed is known to be eventually zero.

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Keywords

Journal Title

Annals of Probability

Conference Name

Journal ISSN

0091-1798
2168-894X

Volume Title

Publisher

Institute of Mathematical Statistics

Publisher DOI

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