Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotics of quantum weighted Hurwitz numbers   This work concerns both the semiclassical and zero temperature asymptotics of
quantum weighted double Hurwitz numbers. The partition function for quantum
weighted double Hurwitz numbers can be interpreted in terms of the energy
distri- bution of a quantum Bose gas with vanishing fugacity. We compute the
leading semi- classical term of the partition function for three versions of
the quantum weighted Hurwitz numbers, as well as lower order semiclassical
corrections. The classical limit $\hbar \ra 0$ is shown to reproduce the simple
single and double Hurwitz numbers studied by Pandharipande and Okounkov
[20,22]. The KP-Toda $\tau$-function that serves as generating function for the
quantum Hurwitz numbers is shown to have the $\tau$-function of [20,22] as its
leading term in the classical limit, and, with suitable scaling, the same holds
for the partition function, the weights and expectations of Hurwitz numbers. We
also compute the zero temperature limit $T \ra 0$ of the partition function and
quantum weighted Hurwitz numbers. The KP or Toda $\tau$-function serving as
generating function for the quantum Hurwitz numbers are shown to give the one
for Belyi curves in the zero temperature limit and, with suitable scaling, the
same holds true for the partition function, the weights and the expectations of
Hurwitz numbers.

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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph