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We answer positively a question of Kaimanovich and Vershik from 1979, showingthat the final configuration of lamps for simple random walk on the lamplightergroup 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 moregeneral types on more general groups.

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