Range and Speed of Rotor Walks on Trees.
J THEOR PROBAB 2020;
33:1657-1690. [PMID:
32879555 PMCID:
PMC7446282 DOI:
10.1007/s10959-019-00904-1]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2018] [Revised: 04/01/2019] [Indexed: 11/27/2022]
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.
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