Range and Speed of Rotor Walks on Trees

Wilfried Huss () and Ecaterina Sava-Huss ()
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Wilfried Huss: ADB Safegate
Ecaterina Sava-Huss: Graz University of Technology

Journal of Theoretical Probability, 2020, vol. 33, issue 3, 1657-1690

Abstract: 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.

Keywords: Rotor walk; Range; Rate of escape; Galton–Watson tree; Generating function; Law of large numbers; Recurrence; Transience; Contour function; 05C81; 60J80; 60F05; 60J10 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-019-00904-1

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