[Statlist] Research Seminar in Statistics *FRIDAY 27 SEPTEMBER 2019* GSEM, University of Geneva

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Dear All,

We are pleased to invite you to our next Research Seminar.

Looking forward to seeing you


Organizers :                                                                                   
E. Cantoni - S. Engelke - D. La Vecchia - E. Ronchetti
S. Sperlich - F. Trojani - M.-P. Victoria-Feser


FRIDAY 27 SEPTEMBER 2019 at 11:15am, Uni-Mail M 5220

Spectral Analysis of Critical Erdös-Renyi Graphs
Antti KNOWLES - University of Geneva, Section of Mathematicsl

ABSTRACT:
The Erdös-Rényi graph G(N,p) is the simplest model of a random graph, where each edge of the complete graph on N vertices is open with probability p, independently of the others. If p = p_N is not too small then the degrees of the graph concentrate with high probability and the graph is homogeneous. On the other hand, for p of order (log N) / N and smaller, the degrees cease to concentrate and the graph is with high probability inhomogeneous, containing isolated vertices, leaves, hubs, etc. I present results on the eigenvalues and eigenvectors of the adjacency matrix of G(N,p) at and below the critical scale. I show a rigidity estimate for the locations of the eigenvalues and explain a transition from localized to delocalized eigenvectors at a specific location in the spectrum.


Visit the website: https://www.unige.ch/gsem/en/research/seminars/rcs/