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arXiv · 1508.01845

Poisson Boundaries of Lamplighter Groups: Proof of the Kaimanovich-Vershik Conjecture

Russell Lyons·Yuval Peres
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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 ${\Bbb Z}^d$ ($d \ge 3$) is the Poisson boundary. For $d \ge 5$, this had been shown earlier by Erschler (2011). We extend this to walks of more general types on more general groups.

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Russell Lyons, Yuval Peres. 2015-08-08. Poisson Boundaries of Lamplighter Groups: Proof of the Kaimanovich-Vershik Conjecture. https://arxiv.org/abs/1508.01845

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