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March 2013 Random Dirichlet environment viewed from the particle in dimension $d\ge3$
Christophe Sabot
Ann. Probab. 41(2): 722-743 (March 2013). DOI: 10.1214/11-AOP699


We consider random walks in random Dirichlet environment (RWDE), which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On ${\mathbb{Z}}^{d}$, RWDE are parameterized by a $2d$-tuple of positive reals called weights. In this paper, we characterize for $d\ge3$ the weights for which there exists an absolutely continuous invariant probability distribution for the process viewed from the particle. We can deduce from this result and from [Ann. Inst. Henri Poincaré Probab. Stat. 47 (2011) 1–8] a complete description of the ballistic regime for $d\ge3$.


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Christophe Sabot. "Random Dirichlet environment viewed from the particle in dimension $d\ge3$." Ann. Probab. 41 (2) 722 - 743, March 2013.


Published: March 2013
First available in Project Euclid: 8 March 2013

zbMATH: 1269.60077
MathSciNet: MR3077524
Digital Object Identifier: 10.1214/11-AOP699

Primary: 60K35 , 60K37

Keywords: Dirichlet distribution , invariant measure viewed from the particle , Random walk in random environment , reinforced random walks

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 2 • March 2013
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