Open Access
2012 Transience and recurrence of rotor-router walks on directed covers of graphs
Wilfried Huss, Ecaterina Sava
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Electron. Commun. Probab. 17: 1-13 (2012). DOI: 10.1214/ECP.v17-2096


The aim of this note is to extend the result of Angel and Holroyd concerning the transience and the recurrence of transfinite rotor-router walks, for random initial configuration of rotors on homogeneous trees. We address the same question on directed covers of finite graphs, which are also called trees with finitely many cone types or periodic trees. Furthermore, we provide an example of a directed cover such that the rotor-router walk can be either recurrent or transient, depending only on the planar embedding of the periodic tree. <strong><a href="">An Erratum is available in ECP volume 19, paper 71, (2014)</a>.</strong>


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Wilfried Huss. Ecaterina Sava. "Transience and recurrence of rotor-router walks on directed covers of graphs." Electron. Commun. Probab. 17 1 - 13, 2012.


Accepted: 22 September 2012; Published: 2012
First available in Project Euclid: 7 June 2016

zbMATH: 1252.05035
MathSciNet: MR2981897
Digital Object Identifier: 10.1214/ECP.v17-2096

Primary: 05C05
Secondary: 05C25 , 82C20

Keywords: directed covers , Graphs , multitype branching process , recurrence , rotor-router walks , transience

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