A note on the Poisson boundary of lamplighter random walks
نویسندگان
چکیده
منابع مشابه
A note on the Poisson boundary of lamplighter random walks
The main goal of this paper is to determine the Poisson boundary of lamplighter random walks over a general class of discrete groups Γ endowed with a “rich” boundary. The starting point is the Strip Criterion of identification of the Poisson boundary for random walks on discrete groups due to Kaimanovich [16]. A geometrical method for constructing the strip as a subset of the lamplighter group ...
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Let Tq be the homogeneous tree with degree q + 1 ≥ 3 and G a finitely generated group whose Cayley graph is Tq. The associated lamplighter group is the wreath product Zr ≀ G, where Zr is the cyclic group of order r. For a large class of random walks on this group, we prove almost sure convergence to a natural geometric boundary. If the probability law governing the random walk has finite first ...
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Suppose we are given an infinite, finitely generated group G and a transient random walk with bounded range on the wreath product (Z/2Z) ≀ G, such that its projection on G is transient. This random walk can be interpreted as a lamplighter random walk, where there is a lamp at each element of G, which can be switched on and off, and a lamplighter walks along G and switches lamps randomly on and ...
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2009
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-009-0103-5