Electronic Journal of Probability

Integrability of exit times and ballisticity for random walks in Dirichlet environment

Laurent Tournier

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Probab., Volume 14 (2009), paper no. 16, 431-451.

Dates
Accepted: 10 February 2009
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819477

Digital Object Identifier
doi:10.1214/EJP.v14-609

Mathematical Reviews number (MathSciNet)
MR2480548

Zentralblatt MATH identifier
1192.60113

Subjects
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)

Keywords
random walks in random environment Dirichlet distribution exit time reinforced random walks quotient graph ballisticity

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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


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References

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