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Random walks in random Dirichlet environment are transient in dimension \(d \geq 3\). (English) Zbl 1231.60121

This paper studies a special class of random walks on infinite regular graphs, where the transition probability vectors on each vertex are random. In this particular paper, they follow the Dirichlet distribution. The underlying graph that is considered is \(\mathbb{Z}^d\) where \(d\geq 3\). The main result of this work is that such a random walk is transient. This result also applies to symmetric graphs of bounded degree, which also include the class of finitely generated Cayley graphs; there, it is known that a simple random walk is transient.

MSC:

60K37 Processes in random environments
60K35 Interacting random processes; statistical mechanics type models; percolation theory
05C20 Directed graphs (digraphs), tournaments
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