Rotor-routing on Galton-Watson trees

Wilfried Huss; Sebastian Mueller; Ecaterina Sava-Huss

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arXiv · 1412.5330

Rotor-routing on Galton-Watson trees

Wilfried Huss·Sebastian Mueller·Ecaterina Sava-Huss

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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, 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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BibTeX RIS

Wilfried Huss, Sebastian Mueller, Ecaterina Sava-Huss. 2014-12-17. Rotor-routing on Galton-Watson trees. https://arxiv.org/abs/1412.5330

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