Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: PDE's for the Gaussian ensemble with external source and the Pearcey
  distribution   The present paper studies a Gaussian Hermitian random matrix ensemble with
external source, given by a fixed diagonal matrix with two eigenvalues a and
-a. As a first result, the probability that the eigenvalues of the ensemble
belong to a set satisfies a fourth order PDE with quartic non-linearity; the
variables being the eigenvalue a and the boundary points of the set. This
equation enables one to find a PDE for the Pearcey distribution. The latter
describes the statistics of the eigenvalues near the closure of a gap; i.e.,
when the support of the equilibrium measure for large size random matrices has
a gap, which can be made to close. Precisely, the Gaussian Hermitian random
matrix ensemble with external source has this feature. In this work, we show
the Pearcey distribution satisfies a a fourth order PDE with cubic
non-linearity. The PDE for the finite problem is found by by showing that an
appropriate integrable deformation of the random matrix ensemble with external
source satisfies the three-component KP equation and Virasoro constraints.

28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th