Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Choquet-Deny theorem and distal properties of totally disconnected
  locally compact groups of polynomial growth   We obtain sufficient and necessary conditions for the Choquet-Deny theorem to
hold in the class of compactly generated totally disconnected locally compact
groups of polynomial growth, and in a larger class of totally disconnected
generalized $\ov{FC}$-groups. The following conditions turn out to be
equivalent when $G$ is a metrizable compactly generated totally disconnected
locally compact group of polynomial growth: (i) the Choquet-Deny theorem holds
for $G$; (ii) the group of inner automorphisms of $G$ acts distally on $G$;
(iii) every inner automorphism of $G$ is distal; (iv) the contraction subgroup
of every inner automorphism of $G$ is trivial; (v) $G$ is a SIN group. We also
show that for every probability measure $\mu$ on a totally disconnected
compactly generated locally compact second countable group of polynomial
growth, the Poisson boundary is a homogeneous space of $G$, and that it is a
compact homogeneous space when the support of $\mu$ generates $G$.

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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: hep-ex