  Random matrices have their roots in multivariate analysis in statistics, and
since Wigner's pioneering work in 1955, they have been a very important tool in
mathematical physics. In functional analysis, random matrices and random
structures have in the last two decades been used to construct Banach spaces
with surprising properties. After Voiculescu in 1990--1991 used random matrices
to classification problems for von Neumann algebras, they have played a key
role in von Neumann algebra theory. In this lecture we will discuss some new
applications of random matrices to operator algebra theory, namely applications
to classification problems for $C^*$-algebras and to the invariant subspace
problem relative to a von Neumann algebra.
