### 2 maj 2005, kl 13.15-14.15, KTH, rum 3721.

### Peter Forrester (University of Melbourne):
Sampling from eigenvalue distributions for matrix ensembles

**Abstract.**
The eigenvalue distributions of Gaussian random matrices and the
random matrices from the classical groups play a fundamental role in
the applications of random matrices. A basic question relates to the
sampling from these distributions: how can it most efficiently be
carried out? Rather than having to generate a random matrix of the
sought type, and then computing its eigenvalues, it is now known that
the characteristic polynomials in question satisfy simple recurrences
with random coefficients. Thus the distributions can be sampled by
computing the characteristic polynomials from the recurrences, and
then computing its zeros. I'll review these developments, and explain
my own contribution. One aspect of the latter (in joint work with
Eric Rains) relates to the eigenvalue distribution of certain rank 1
perturbations, or equivalently the zeros of some random rational
functions.