Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cumulants of the q-semicircular law, Tutte polynomials, and heaps   The q-semicircular distribution is a probability law that interpolates
between the Gaussian law and the semicircular law. There is a combinatorial
interpretation of its moments in terms of matchings where q follows the number
of crossings, whereas for the free cumulants one has to restrict the
enumeration to connected matchings. The purpose of this article is to describe
combinatorial properties of the classical cumulants. We show that like the free
cumulants, they are obtained by an enumeration of connected matchings, the
weight being now an evaluation of the Tutte polynomial of a so-called crossing
graph. The case q=0 of these cumulants was studied by Lassalle using symmetric
functions and hypergeometric series. We show that the underlying combinatorics
is explained through the theory of heaps, which is Viennot's geometric
interpretation of the Cartier-Foata monoid. This method also gives results for
the classical cumulants of the free Poisson law.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
16
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: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys