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

   
@article{EJP609,
	author = {Laurent Tournier},
	title = {Integrability of exit times and ballisticity for random walks in Dirichlet environment},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {14},
	year = {2009},
	keywords = {random walks in random environment; Dirichlet distribution; exit time; reinforced random walks; quotient graph; ballisticity},
	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.},
	pages = {no. 16, 431-451},
	issn = {1083-6489},
	doi = {10.1214/EJP.v14-609},    
        url = {http://ejp.ejpecp.org/article/view/609}}