Rotor-routing on Galton-Watson trees

Wilfried Huss, Sebastian Mueller, Ecaterina Sava-Huss

Published 2014-12-17Version 1

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, and and give a classification in recurrence and transience for transfinite rotor-router walks on these trees.