 |
|
|
| | | | | |
|
|
|
|
|
Integrability of exit times and ballisticity for random walks in Dirichlet environment
|
Laurent Tournier, Institut Camille Jordan, Universite Lyon 1
|
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.
|
Full text: PDF
Pages: 431-451
Published on: February 10, 2009
|
Bibliography
-
Enriquez, Nathanaël; Sabot, Christophe. Edge oriented reinforced random walks and RWRE.
C. R. Math. Acad. Sci. Paris 335 (2002), no. 11, 941--946. MR1952554 (2004c:60272)
-
Enriquez, Nathanaël; Sabot, Christophe. Random walks in a Dirichlet environment.
Electron. J. Probab. 11 (2006), no. 31, 802--817 (electronic). MR2242664 (2007m:60306)
-
Kalikow, Steven A. Generalized random walk in a random environment.
Ann. Probab. 9 (1981), no. 5, 753--768. MR0628871 (84c:60101)
-
Pemantle, Robin. A survey of random processes with reinforcement.
Probab. Surv. 4 (2007), 1--79 (electronic). MR2282181 (2007k:60230)
-
Sabot, Christophe. Ballistic random walks in random environment at low disorder.
Ann. Probab. 32 (2004), no. 4, 2996--3023. MR2094437 (2005g:60166)
-
Solomon, Frederick. Random walks in a random environment.
Ann. Probab. 3 (1975), 1--31.
Math. Review number not available.
-
Sznitman, Alain-Sol; Zerner, Martin. A law of large numbers for random walks in random environment.
Ann. Probab. 27 (1999), no. 4, 1851--1869. MR1742891 (2001f:60116)
-
Sznitman, Alain-Sol. On a class of transient random walks in random environment.
Ann. Probab. 29 (2001), no. 2, 724--765. MR1849176 (2004b:60234)
-
Sznitman, Alain-Sol. An effective criterion for ballistic behavior of random walks in random environment.
Probab. Theory Related Fields 122 (2002), no. 4, 509--544. MR1902189 (2003c:60168)
-
Wilks, Samuel S. Mathematical statistics.
A Wiley Publication in Mathematical Statistics John Wiley & Sons, Inc., New York-London 1962 xvi+644 pp. MR0144404 (26 #1949)
|
|
|
|
|
|
|
|
| | | | |
Electronic Journal of Probability. ISSN: 1083-6489 |
|
Context