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2009 Integrability of exit times and ballisticity for random walks in Dirichlet environment
Laurent Tournier
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Electron. J. Probab. 14: 431-451 (2009). DOI: 10.1214/EJP.v14-609


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.


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Laurent Tournier. "Integrability of exit times and ballisticity for random walks in Dirichlet environment." Electron. J. Probab. 14 431 - 451, 2009.


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

zbMATH: 1192.60113
MathSciNet: MR2480548
Digital Object Identifier: 10.1214/EJP.v14-609

Primary: 60K37
Secondary: 60J10 , 82D30

Keywords: Ballisticity , Dirichlet distribution , Exit time , quotient graph , random walks in random environment , reinforced random walks

Vol.14 • 2009
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