Poisson boundaries of lamplighter groups: proof of the Kaimanovich–Vershik conjecture
Russell Lyons
Indiana University, Bloomington, USAYuval Peres
Kent State University, USA
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Abstract
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 is the Poisson boundary. For , this had been shown earlier by Erschler (2011). We extend this to walks of more general types on more general groups.
Cite this article
Russell Lyons, Yuval Peres, Poisson boundaries of lamplighter groups: proof of the Kaimanovich–Vershik conjecture. J. Eur. Math. Soc. 23 (2021), no. 4, pp. 1133–1160
DOI 10.4171/JEMS/1030