Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectra of random Hermitian matrices with a small-rank external source:
  supercritical and subcritical regimes   Random Hermitian matrices with a source term arise, for instance, in the
study of non-intersecting Brownian walkers \cite{Adler:2009a, Daems:2007} and
sample covariance matrices \cite{Baik:2005}.
  We consider the case when the $n\times n$ external source matrix has two
distinct real eigenvalues: $a$ with multiplicity $r$ and zero with multiplicity
$n-r$. The source is small in the sense that $r$ is finite or $r=\mathcal
O(n^\gamma)$, for $0< \gamma<1$. For a Gaussian potential, P\'ech\'e
\cite{Peche:2006} showed that for $|a|$ sufficiently small (the subcritical
regime) the external source has no leading-order effect on the eigenvalues,
while for $|a|$ sufficiently large (the supercritical regime) $r$ eigenvalues
exit the bulk of the spectrum and behave as the eigenvalues of $r\times r$
Gaussian unitary ensemble (GUE). We establish the universality of these results
for a general class of analytic potentials in the supercritical and subcritical
regimes.

36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con