Electronic Journal of Probability
- Electron. J. Probab.
- Volume 14 (2009), paper no. 16, 431-451.
Integrability of exit times and ballisticity for random walks in Dirichlet environment
We consider random walks in Dirichlet random environment. Since the Dirichlet distribution is not uniformly elliptic, the annealed integrability of the exit time out of a given finite subset is a non-trivial question. In this paper we provide a simple and explicit equivalent condition for the integrability of Green functions and exit times on any finite directed graph. The proof relies on a quotienting procedure allowing for an induction argument on the cardinality of the graph. This integrability problem arises in the definition of Kalikow auxiliary random walk. Using a particular case of our condition, we prove a refined version of the ballisticity criterion given by Enriquez and Sabot.
Electron. J. Probab., Volume 14 (2009), paper no. 16, 431-451.
Accepted: 10 February 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: 60K37: Processes in random environments
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 82D30: Random media, disordered materials (including liquid crystals and spin glasses)
This work is licensed under aCreative Commons Attribution 3.0 License.
Tournier, Laurent. Integrability of exit times and ballisticity for random walks in Dirichlet environment. Electron. J. Probab. 14 (2009), paper no. 16, 431--451. doi:10.1214/EJP.v14-609. https://projecteuclid.org/euclid.ejp/1464819477