Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finitary Coloring   Suppose that the vertices of ${\mathbb Z}^d$ are assigned random colors via a
finitary factor of independent identically distributed (iid) vertex-labels.
That is, the color of vertex $v$ is determined by a rule that examines the
labels within a finite (but random and perhaps unbounded) distance $R$ of $v$,
and the same rule applies at all vertices. We investigate the tail behavior of
$R$ if the coloring is required to be proper (that is, if adjacent vertices
must receive different colors). When $d\geq 2$, the optimal tail is given by a
power law for 3 colors, and a tower (iterated exponential) function for 4 or
more colors (and also for 3 or more colors when $d=1$). If proper coloring is
replaced with any shift of finite type in dimension 1, then, apart from trivial
cases, tower function behavior also applies.

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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
1
The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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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: eess
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas