Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Real spectra of large real asymmetric random matrices   When a randomness is introduced at the level of real matrix elements,
depending on its particular realization, a pair of eigenvalues can appear as
real or form a complex conjugate pair. We show that in the limit of large
matrix size the density of such real eigenvalues is proportional to the square
root of the asymptotic density of complex eigenvalues continuated to the real
line. This relation allows one to calculate the real densities up to a
normalization constant, which is then applied to various examples, including
heavy-tailed ensembles and adjacency matrices of sparse random regular graphs.

7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph