Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A representation of joint moments of CUE characteristic polynomials in
  terms of Painleve functions   We establish a representation of the joint moments of the characteristic
polynomial of a CUE random matrix and its derivative in terms of a solution of
the sigma-Painleve V equation. The derivation involves the analysis of a
formula for the joint moments in terms of a determinant of generalised Laguerre
polynomials using the Riemann-Hilbert method. We use this connection with the
sigma-Painleve V equation to derive explicit formulae for the joint moments and
to show that in the large-matrix limit the joint moments are related to a
solution of the sigma-Painleve III equation. Using the conformal block
expansion of the tau-functions associated with the sigma-Painleve V and the
sigma-Painleve III equations leads to general conjectures for the joint
moments.

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The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: q-fin
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an