Escape Rates for Rotor Walks in Zd

Rotor walk is a deterministic analogue of random walk. We study its recurrence and transience properties on Z d for the initial conguration 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= logn in dimension 2.