Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 20 (2015), paper no. 49, 12 pp.
Rotor-routing on Galton-Watson trees
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.
Electron. Commun. Probab., Volume 20 (2015), paper no. 49, 12 pp.
Accepted: 29 June 2015
First available in Project Euclid: 7 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 05C81: Random walks on graphs 05C05: Trees 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]
This work is licensed under a Creative Commons Attribution 3.0 License.
Huss, Wilfried; Müller, Sebastian; Sava-Huss, Ecaterina. Rotor-routing on Galton-Watson trees. Electron. Commun. Probab. 20 (2015), paper no. 49, 12 pp. doi:10.1214/ECP.v20-4000. https://projecteuclid.org/euclid.ecp/1465320976