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DTSTART;VALUE=DATE:20170425T171500
DTEND;VALUE=DATE:20170425T171500
UID:5763@agenda.unifr.ch
DESCRIPTION:I review some recent work on the extreme eigenvalues of sparse random graphs, such as inhomogeneous Erdos-Renyi graphs. Let n denote the number of vertices and d the maximal mean degree. We establish a crossover in the behaviour of the extreme eigenvalues at the scale $d = log$  $n$. For $d >> log$ $n$ we prove that the extreme eigenvalues converge to the edges of the support of the asymptotic eigenvalue distribution. For $d << log$ $n$, we prove that these extreme eigenvalues are governed by the largest degrees, and that they exhibit a novel behaviour, which in particular rules out their convergence to a nondegenerate point process.
SUMMARY:Prof. Antti Knowles (Uni Genève): Extreme eigenvalues of sparse random graphs
CATEGORIES:Colloque / Congrès / Forum
LOCATION:PER 08\, Phys 2.52\, Chemin du Musée 3\, 1700 Fribourg
URL;VALUE=URI:https://agenda.unifr.ch/e/fr/5763
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