Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Contact Graphs, Boundaries, and a Central Limit Theorem for CAT(0)
  cubical complexes   Let $X$ be a nonelementary CAT(0) cubical complex. We prove that if $X$ is
essential, irreducible, then the contact graph of $X$ (introduced in
\cite{Hagen}) is unbounded and its boundary is homeomorphic to the regular
boundary of $X$ (defined in \cite{Fernos}, \cite{KarSageev}). Using this, we
reformulate the Caprace- Sageev's Rank-Rigidity Theorem in terms of the action
on the contact graph. Let $G$ be a group with a nonelementary action on $X$,
and $(Z_n)$ a random walk on $G$ with finite second moment. Using this
identification of the boundary of the contact graph, we prove a Central Limit
Theorem for $(Z_n)$, namely that $\frac{d(Z_n o,o)-nA}{\sqrt n}$ converges in
law to a non-degenerate Gaussian distribution (where $A=\lim
\frac{d(Z_no,o)}{n}$ is the drift of the random walk, and $o\in X$ is an
arbitrary basepoint).

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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat