## Electronic Communications in Probability

- Electron. Commun. Probab.
- Volume 17 (2012), paper no. 41, 13 pp.

### Transience and recurrence of rotor-router walks on directed covers of graphs

Wilfried Huss and Ecaterina Sava

#### Abstract

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="http://dx.doi.org/10.1214/ECP.v19-3848">An Erratum is available in ECP volume 19, paper 71, (2014)</a>.</strong>

#### Article information

**Source**

Electron. Commun. Probab., Volume 17 (2012), paper no. 41, 13 pp.

**Dates**

Accepted: 22 September 2012

First available in Project Euclid: 7 June 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.ecp/1465263174

**Digital Object Identifier**

doi:10.1214/ECP.v17-2096

**Mathematical Reviews number (MathSciNet)**

MR2981897

**Zentralblatt MATH identifier**

1252.05035

**Subjects**

Primary: 05C05: Trees

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 82C20: Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs

**Keywords**

graphs directed covers rotor-router walks multitype branching process recurrence transience

**Rights**

This work is licensed under a Creative Commons Attribution 3.0 License.

#### Citation

Huss, Wilfried; Sava, Ecaterina. Transience and recurrence of rotor-router walks on directed covers of graphs. Electron. Commun. Probab. 17 (2012), paper no. 41, 13 pp. doi:10.1214/ECP.v17-2096. https://projecteuclid.org/euclid.ecp/1465263174