Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral distributions of adjacency and Laplacian matrices of random
  graphs   In this paper, we investigate the spectral properties of the adjacency and
the Laplacian matrices of random graphs. We prove that: (i) the law of large
numbers for the spectral norms and the largest eigenvalues of the adjacency and
the Laplacian matrices; (ii) under some further independent conditions, the
normalized largest eigenvalues of the Laplacian matrices are dense in a compact
interval almost surely; (iii) the empirical distributions of the eigenvalues of
the Laplacian matrices converge weakly to the free convolution of the standard
Gaussian distribution and the Wigner's semi-circular law; (iv) the empirical
distributions of the eigenvalues of the adjacency matrices converge weakly to
the Wigner's semi-circular law.

30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph