Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral Statistics of Lattice Graph Structured, Non-uniform
  Percolations   Design of filters for graph signal processing benefits from knowledge of the
spectral decomposition of matrices that encode graphs, such as the adjacency
matrix and the Laplacian matrix, used to define the shift operator. For shift
matrices with real eigenvalues, which arise for symmetric graphs, the empirical
spectral distribution captures the eigenvalue locations. Under realistic
circumstances, stochastic influences often affect the network structure and,
consequently, the shift matrix empirical spectral distribution. Nevertheless,
deterministic functions may often be found to approximate the asymptotic
behavior of empirical spectral distributions of random matrices. This paper
uses stochastic canonical equation methods developed by Girko to derive such
deterministic equivalent distributions for the empirical spectral distributions
of random graphs formed by structured, non-uniform percolation of a
D-dimensional lattice supergraph. Included simulations demonstrate the results
for sample parameters.

11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th