Skip to Main content Skip to Navigation
Conference papers

Characterization of Random Matrix Eigenvectors for Stochastic Block Model

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.
Document type :
Conference papers
Complete list of metadata

Cited literature [15 references]  Display  Hide  Download

https://hal.inria.fr/hal-01258664
Contributor : Konstantin Avrachenkov <>
Submitted on : Tuesday, January 19, 2016 - 12:46:24 PM
Last modification on : Monday, March 29, 2021 - 2:47:23 PM
Long-term archiving on: : Friday, November 11, 2016 - 11:57:56 AM

File

Asilomar15.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01258664, version 1

Collections

Citation

Arun Kadavankandy, Laura Cottatellucci, Konstantin Avrachenkov. Characterization of Random Matrix Eigenvectors for Stochastic Block Model. 49th Asilomar Conference on Signals, Systems, and Computer, Nov 2015, Pacific Grove, CA, United States. ⟨hal-01258664⟩

Share

Metrics

Record views

339

Files downloads

466