Rotor-routing on Galton-Watson trees

Ecaterina Sava-Huss, Wilfried Huss, Sebastian Müller

Research output: Contribution to journalArticle

Abstract

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.
Original languageEnglish
Article number49
Number of pages12
JournalElectronic Communications in Probability
Volume20
Publication statusPublished - 2015

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