Strong convergence of random matrices with latent geometries

Vienna Probability Seminar

We will present recent results on the convergence of the operator norm of random matrices of large dimension. Our random matrices are build by taking tensor products of deterministic matrices and independent Haar distributed unitary matrices or independent random permutation matrices. This class of random matrices allows for example to consider random Schreier graphs of Cartesian products of free groups. They are motivated by questions in operator algebra, representation theory and spectral graph theory.  The talk will be notably based on joint works with Benoit Collins.