Graduate School and Research Center in Digital Sciences

Spectral properties of random matrices for stochastic block model

Avrachenkov, Konstantin; Cottatellucci, Laura; Kadavankandy, Arun

PHYSCOMNET 2015, International Workshop on Physics-Inspired Paradigms in Wireless Communications and Networks (In WiOpt 2015), 29 May 2015, Mumbai, India

We consider an extension of Erdös-Rényi graph known in literature as Stochastic Block Model (SBM).We analyze the limiting empirical distribution of the eigenvalues of the adjacency matrix of SBM. We derive a fixed point equation for the Stieltjes transform of the limiting eigenvalue empirical distribution function (e.d.f.), concentration results on both the support of the limiting e.s.f. and the extremal eigenvalues outside the support of the limiting e.d.f. Additionally, we derive analogous results for the normalized Laplacian matrix and discuss potential applications of the general results in epidemics and random walks.

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Title:Spectral properties of random matrices for stochastic block model
Keywords:Spectral Graph Theory, Random Graphs, Random Matrices,Stochastic Block Model
Type:Invited paper in a conference
Department:Communication systems
Eurecom ref:4535
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Bibtex: @inproceedings{EURECOM+4535, doi = {}, year = {2015}, title = {{S}pectral properties of random matrices for stochastic block model}, author = {{A}vrachenkov, {K}onstantin and {C}ottatellucci, {L}aura and {K}adavankandy, {A}run}, booktitle = {{PHYSCOMNET} 2015, {I}nternational {W}orkshop on {P}hysics-{I}nspired {P}aradigms in {W}ireless {C}ommunications and {N}etworks ({I}n {W}i{O}pt 2015), 29 {M}ay 2015, {M}umbai, {I}ndia}, address = {{M}umbai, {INDIA}}, month = {05}, url = {} }
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