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Escape rates for rotor walk in Z^d

Rotor walk is a deterministic analogue of random walk. We study its recurrence and transience properties on Z^d for the initial configuration of all rotors aligned. If n particles in turn perform rotor walks starting from the origin, we show that the number that escape (i.e., never return to the origin) is of order n in dimensions d>=3, and of order n/log(n) in dimension 2.

preprint2013arXivOpen access
Laura FlorescuShirshendu GangulyLionel LevineYuval Peres
math.COcond-mat.stat-mechmath.PR
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Laura FlorescuShirshendu GangulyLionel LevineYuval Peres

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