Range and Speed of Rotor Walks on Trees

Abstract

We prove a law of large numbers for the range of rotor walks with random initial configuration on regular trees and on Galton-Watson trees. We also show the existence of the speed for such rotor walks. More precisely, we show that on the classes of trees under consideration, even in the case when the rotor walk is recurrent, the range grows at linear speed.

Limit theorems for discrete multitype branching processes counted with a characteristic

“…The investigation of such processes has yet another motivation in the context of rotor walks with random initial configuration on trees, see [8,9,10]. In these papers the authors investigate law of large numbers for a class of processes called rotor walks, processes that interpolate between random walks and deterministic walks; see also [7] for a functional limit theorem of the interpolated processes.…”