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Spectral statistics of lattice graph structured, non-uniform percolations
- Source :
- ICASSP
- Publication Year :
- 2017
- Publisher :
- IEEE, 2017.
-
Abstract
- 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.<br />ICASSP 2017
- Subjects :
- Random graph
Mathematical analysis
Computer Science - Numerical Analysis
020206 networking & telecommunications
Numerical Analysis (math.NA)
02 engineering and technology
01 natural sciences
010104 statistics & probability
Integer matrix
Matrix (mathematics)
Graph energy
FOS: Mathematics
0202 electrical engineering, electronic engineering, information engineering
Statistical physics
Adjacency matrix
0101 mathematics
Laplacian matrix
Random matrix
Eigenvalues and eigenvectors
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- Accession number :
- edsair.doi.dedup.....09f0316f58137220cdd429ca2a46a624