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


 
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1. Title Title of document Integrability of exit times and ballisticity for random walks in Dirichlet environment
 
2. Creator Author's name, affiliation, country Laurent Tournier; Institut Camille Jordan, Universite Lyon 1
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) random walks in random environment; Dirichlet distribution; exit time; reinforced random walks; quotient graph; ballisticity
 
3. Subject Subject classification 60K37; 60J10 ; 82D30
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ANR project MEMEMO
 
7. Date (YYYY-MM-DD) 2009-02-10
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/609
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-609
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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