Mobility Edge for Lévy Matrices

Lévy matrices are symmetric random matrices whose entries are in the domain of attraction of an \alpha stable law. For \alpha < 1, it had been predicted that these matrices exhibit an Anderson transition, also called a mobility edge, a point in the spectrum where eigenvector behavior sharply transitions from delocalized to localized. In this talk, we describe recent results that establish the existence and also explicitly compute the location of this mobility edge for Lévy matrices. This is based on joint work with Charles Bordenave and Patrick Lopatto.