Abstract
I will review the role of the quantum unique ergodicity (QUE) notion of delocalization, in the context of random matrices. QUE can be proved by dynamic or combinatorial methods, and implies that the local eigenvalues statistics exhibit the universal repulsion of Gaussian, invariant ensembles.We will focus in particular on the techniques involving the Dyson Brownian Motion.
Applications include Wigner matrices, Erdös Rényi and d-regular random graphs, and random band matrices.
