Graduate School and Research Center in Digital Sciences

Characterization of random Matrix eigenvectors for stochastic block model

Kadavankandy, Arun; Cottatellucci, Laura; Avrachenkov, Konstantin

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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Title:Characterization of random Matrix eigenvectors for stochastic block model
Type:Invited paper in a conference
Department:Communication systems
Eurecom ref:4780
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Bibtex: @inproceedings{EURECOM+4780, doi = {}, year = {2015}, title = {{C}haracterization of random {M}atrix eigenvectors for stochastic block model}, author = {{K}adavankandy, {A}run and {C}ottatellucci, {L}aura and {A}vrachenkov, {K}onstantin}, booktitle = {{ASILOMAR} 2015, 49th {A}silomar {C}onference on {S}ignals, {S}ystems, and {C}omputers, {N}ovember 8-11, 2015, {P}acific {G}rove, {CA}, {USA} }, address = {{A}silomar, {UNITED} {STATES}}, month = {11}, url = {} }
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