Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lectures on the Asymptotic Expansion of a Hermitian Matrix Integral   In these lectures three different methods of computing the asymptotic
expansion of a Hermitian matrix integral is presented. The first one is a
combinatorial method using Feynman diagrams. This leads us to the generating
function of the reciprocal of the order of the automorphism group of a tiling
of a Riemann surface. The second method is based on the classical analysis of
orthogonal polynomials. A rigorous asymptotic method is established, and a
special case of the matrix integral is computed in terms of the Riemann
$\zeta$-function. The third method is derived from a formula for the
$\tau$-function solution to the KP equations. This method leads us to a new
class of solutions of the KP equations that are
  \emph{transcendental}, in the sense that they cannot be obtained by the
celebrated Krichever construction and its generalizations based on algebraic
geometry of vector bundles on Riemann surfaces. In each case a mathematically
rigorous way of dealing with asymptotic series in an infinite number of
variables is established.

18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
3
The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin