Event Details

Large deviations for the largest eigenvalue of the addition of random matrices

A and B being two Hermitian matrices with a given spectrum, the description of the spectrum of their sum A+B is a classical and difficult problem. If we assume that the eigenvectors of B are "in generic position" with respect to those of A, free probability theory provides very powerful tools to describe - at least asymptotically - the spectrum of the sum. We will present some of these tools and address the problem of understanding the behavior of the largest eigevalue of the sum, in particular its large deviations. This is joint work with Alice Guionnet (CNRS and ENS Lyon)