Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The generating function for the Bessel point process and a system of
  coupled Painlev\'{e} V equations   We study the joint probability generating function for $k$ occupancy numbers
on disjoint intervals in the Bessel point process. This generating function can
be expressed as a Fredholm determinant. We obtain an expression for it in terms
of a system of coupled Painlev\'{e} V equations, which are derived from a Lax
pair of a Riemann-Hilbert problem. This generalizes a result of Tracy and Widom
[24], which corresponds to the case $k = 1$. We also provide some examples and
applications. In particular, several relevant quantities can be expressed in
terms of the generating function, like the gap probability on a union of
disjoint bounded intervals, the gap between the two smallest particles, and
large $n$ asymptotics for $n\times n$ Hankel determinants with a Laguerre
weight possessing several jumps discontinuities near the hard edge.

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The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
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The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
34
The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
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The categories of this paper are: cs
30
The categories of this paper are: q-alg