Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random walks on groups and KMS states   A classical construction associates to a transient random walk on a discrete
group $\Gamma$ a compact $\Gamma$-space $\partial_M \Gamma$ known as the Martin
boundary. The resulting crossed product $C^*$-algebra $C(\partial_M \Gamma)
\rtimes_r \Gamma$ comes equipped with a one-parameter group of automorphisms
given by the Martin kernels that define the Martin boundary. In this paper we
study the KMS states for this flow and obtain a complete description when the
Poisson boundary of the random walk is trivial and when $\Gamma$ is a torsion
free non-elementary hyperbolic group. We also construct examples to show that
the structure of the KMS states can be more complicated beyond these cases.

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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc