Poisson Boundaries of Lamplighter Groups : Proof of the Kaimanovich - Vershik Conjecture
نویسندگان
چکیده
We answer positively a question of Kaimanovich and Vershik from 1979, showing that the final configuration of lamps for simple random walk on the lamplighter group over Z (d ≥ 3) is the Poisson boundary. For d ≥ 5, this had been shown earlier by Erschler (2011). We extend this to walks of more general types on more general groups.
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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