Electronic Journal of Probability
- Electron. J. Probab.
- Volume 14 (2009), paper no. 55, 1628-1669.
Recurrence and transience of a multi-excited random walk on a regular tree
We study a model of multi-excited random walk on a regular tree which generalizes the models of the once excited random walk and the digging random walk introduced by Volkov (2003). We show the existence of a phase transition and provide a criterion for the recurrence/transience property of the walk. In particular, we prove that the asymptotic behaviour of the walk depends on the order of the excitations, which contrasts with the one dimensional setting studied by Zerner (2005). We also consider the limiting speed of the walk in the transient regime and conjecture that it is not a monotonic function of the environment.
Electron. J. Probab., Volume 14 (2009), paper no. 55, 1628-1669.
Accepted: 9 July 2009
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F20: Zero-one laws
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
This work is licensed under aCreative Commons Attribution 3.0 License.
Basdevant, Anne-Laure; Singh, Arvind. Recurrence and transience of a multi-excited random walk on a regular tree. Electron. J. Probab. 14 (2009), paper no. 55, 1628--1669. doi:10.1214/EJP.v14-672. https://projecteuclid.org/euclid.ejp/1464819516