Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost-Hermitian Random Matrices: Eigenvalue Density in the Complex
  Plane   We consider an ensemble of large non-Hermitian random matrices of the form
$\hat{H}+i\hat{A}_s$, where $\hat{H}$ and $\hat{A}_s$ are Hermitian
statistically independent random $N\times N$ matrices. We demonstrate the
existence of a new nontrivial regime of weak non-Hermiticity characterized by
the condition that the average of $N\mbox{Tr} \hat{A}_s^2$ is of the same order
as that of $\mbox{Tr} \hat{H}^2 $ when $N\to \infty$. We find explicitly the
density of complex eigenvalues for this regime in the limit of infinite matrix
dimension. The density determines the eigenvalue distribution in the crossover
regime between random Hermitian matrices whose real eigenvalues are distributed
according to the Wigner semi-circle law and random complex matrices whose
eigenvalues are distributed in the complex plane according to the so-called
``elliptic law''.

36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph