Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral statistics for product matrix ensembles of Hermite type with
  external source   We continue investigating spectral properties of a Hermitised random matrix
product, which, contrary to previous product ensembles, allows for eigenvalues
on the full real line. When a GUE matrix with an external source is involved,
we prove that the eigenvalues of the product form a determinantal point process
and derive a double integral representation for correlation kernel. As the
source changes, we observe a critical value and establish the existence of a
phase transition for scaled eigenvalues at the origin. Particularly in the
critical case, we obtain a new family of Pearcey-type kernels.

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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio