Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poisson Boundaries of Lamplighter Groups: Proof of the
  Kaimanovich-Vershik Conjecture   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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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph