Random matrix theory in the Anderson model

The Anderson tight-binding model describes the transport of quantum particles in disordered environments.  A central question in this model is to understand whether, in the long-time limit, particles diffuse out to infinity or else remain trapped in some bounded region.  In this talk, I will describe an approach to understanding this model based on random matrix theory.  With the help of a dispersive estimate, we are able to demonstrate diffusive transport without the need for diagrammatic arguments.