Name
Abstract | ||
|---|---|---|
The eigenvalue spectrum of the adjacency matrix of Stochastic Block Model (SBM) consists of two parts: a finite discrete set of dominant eigenvalues and a continuous bulk of eigenvalues. We characterize analytically the eigenvectors corresponding to the continuous part: the bulk eigenvectors. For symmetric SBM adjacency matrices, the eigenvectors are shown to satisfy two key properties. A modified spectral function of the eigenvalues, depending on the eigenvectors, converges to the eigenvalue spectrum. Its fluctuations around this limit converge to a Gaussian process different from a Brownian bridge. This latter fact disproves that the bulk eigenvectors are Haar distributed. |
Year | Venue | Field |
|---|---|---|
2015 | 2015 49TH ASILOMAR CONFERENCE ON SIGNALS, SYSTEMS AND COMPUTERS | Mathematical optimization,Eigenvalue perturbation,Diagonalizable matrix,Jacobi eigenvalue algorithm,Defective matrix,Eigenvalues and eigenvectors of the second derivative,Modal matrix,Mathematics,Eigenvalues and eigenvectors,Matrix differential equation |
DocType | Citations | PageRank |
Conference | 0 | 0.34 |
References | Authors | |
3 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Arun Kadavankandy | 1 | 6 | 1.67 |
| Laura Cottatellucci | 2 | 272 | 31.04 |
| Konstantin Avrachenkov | 3 | 1250 | 126.17 |