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Seminários do IMPA

Probabilidade e Combinatória

Título
Extreme eigenvalues of Erdös-Rényi graphs
Expositor
Florent Benaych-Georges

Université Paris Descarte
Data
Segunda-feira, 5 de fevereiro de 2018, 15:30
Local
Sala 228
Resumo

In this talk, we shall present some recent works with Charles Bordenave and Antti Knowles giving estimates for the extreme eigenvalues of the centered adjacency matrices of a possibly inhomogenous Erdös-Rényi graph. In the case of the Stochastic Block Model, these works allow to assess the accuracy of the spectral clustering algorithm, whereas in the case of an homogenous Erdös-Rényi graph, they establish a transition between a compact spectrum and a diffuse one, at a threshold which coincides with the connectivity threshold.