Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rate of Escape on the Lamplighter Tree   Suppose we are given a homogeneous tree $\mathcal{T}_q$ of degree $q\geq 3$,
where at each vertex sits a lamp, which can be switched on or off. This
structure can be described by the wreath product $(\mathbb{Z}/2)\wr \Gamma$,
where $\Gamma=\ast_{i=1}^q \mathbb{Z}/2$ is the free product group of $q$
factors $\mathbb{Z}/2$. We consider a transient random walk on a Cayley graph
of $(\mathbb{Z}/2)\wr \Gamma$, for which we want to compute lower and upper
bounds for the rate of escape, that is, the speed at which the random walk
flees to infinity.

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The categories of this paper are: eess
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
3
The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph