Title: Sums of projections with random coefficients.

Abstract: I will discuss aspects of spectral theory of infinite sums of the form $\sum_n \kappa_n P_n$, where $P_n$ are rank one projections in a Hilbert space (not necessarily orthogonal to one another), and $\kappa_n$ are i.i.d. random variables. This problem can be considered as an “abstract version” of the Anderson model. This is recent joint work with Leonid Pastur.