ASILOMAR 2015, 49th Asilomar Conference on Signals, Systems, and Computers, November 8-11, 2015, Pacific Grove, CA, USA
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.
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Systèmes de Communication
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