Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Painlev\'{e} Transcendents and the Hankel Determinants Generated by a
  Discontinuous Gaussian Weight   This paper studies the Hankel determinants generated by a discontinuous
Gaussian weight with one and two jumps. It is an extension of Chen and
Pruessner \cite{Chen2005}, in which they studied the discontinuous Gaussian
weight with a single jump. By using the ladder operator approach, we obtain a
series of difference and differential equations to describe the Hankel
determinant for the single jump case. These equations include the Chazy II
equation, continuous and discrete Painlev\'{e} IV. In addition, we consider the
large $n$ behavior of the corresponding orthogonal polynomials and prove that
they satisfy the biconfluent Heun equation. We also consider the jump at the
edge under a double scaling, from which a Painlev\'{e} XXXIV appeared.
Furthermore, we study the Gaussian weight with two jumps, and show that a
quantity related to the Hankel determinant satisfies a two variables'
generalization of the Jimbo-Miwa-Okamoto $\sigma$ form of the Painlev\'{e} IV.

19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th