KTH Matematik |
Tid: 15 maj 2017 kl 15.15-16.15. Seminarierummet 3721, Institutionen för matematik, KTH, Lindstedtsvägen 25, plan 7. Karta!Föredragshållare: Antti Knowles, Geneva Titel: Extreme eigenvalues of sparse random graphs Abstract 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. Joint work with Florent Benaych-Georges and Charles Bordenave. |
Sidansvarig: Filip Lindskog Uppdaterad: 25/02-2009 |