Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Annular non-crossing permutations and partitions, and second-order
  asymptotics for random matrices   We study the set $S_{ann-nc}$ of permutations of $\{1, ..., p+q \}$ which are
non-crossing in an annulus with $p$ points marked on its external circle and
$q$ points marked on its internal circle. The algebraic approach to
$S_{ann-nc}$ goes by identifying three possible crossing patterns in an
annulus, and by defining a permutation to be annular non-crossing when it does
not display any of these patterns. We prove the annular counterpart for a
``geodesic condition'' shown by Biane to characterize non-crossing permutations
in a disc. We point out that, as a consequence, annular non-crossing
permutations appear in the description of the second order asymptotics for the
joint moments of certain families (Wishart and GUE) of random matrices. We
examine the relation between $S_{ann-nc}$ and the set $NC_{ann}$ of annular
non-crossing partitions of $\{1, ..., p+q \}$, and observe that (unlike in the
disc case) the natural map from $S_{ann-nc}$ onto $NC_{ann}$ has a pathology
which prevents it from being injective.

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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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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: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: econ