Open Access
2015 Rotor-routing on Galton-Watson trees
Wilfried Huss, Sebastian Müller, Ecaterina Sava-Huss
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Electron. Commun. Probab. 20: 1-12 (2015). DOI: 10.1214/ECP.v20-4000


A rotor-router walk on a graph is a deterministic process, in which each vertex is endowed with a rotor that points to one of the neighbors. A particle located at some vertex first rotates the rotor in a prescribed order, and then it is routed to the neighbor the rotor is now pointing at. In the current work we make a step toward in understanding the behavior of rotor router walks on random trees. More precisely, we consider random i.i.d. initial configurations of rotors on Galton-Watson trees T, i.e. on a family tree arising from a Galton-Watson process, and give a classification in recurrence and transience for rotor-router walks on these trees.


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Wilfried Huss. Sebastian Müller. Ecaterina Sava-Huss. "Rotor-routing on Galton-Watson trees." Electron. Commun. Probab. 20 1 - 12, 2015.


Accepted: 29 June 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1321.60177
MathSciNet: MR3367899
Digital Object Identifier: 10.1214/ECP.v20-4000

Primary: 60J80
Secondary: 05C05 , 05C25 , 05C81

Keywords: Galton-Watson trees , recurrence , return probability , rotor-router walk , transience

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