# Matrix models for circular ensembles

## Irina Nenciu

**Abstract: **

We describe an ensemble of (sparse) random matrices whose eigenvalues
follow the Gibbs distribution

for n particles of the Coulomb gas on the
unit circle at inverse temperature beta. Our approach combines

elements from the theory of orthogonal polynomials on the unit circle with
ideas from recent work of

Dumitriu and Edelman. In particular, we resolve
a question left open by them: find a tri-diagonal model

for the Jacobi
ensemble

(Joint work with Rowan Killip. IMRN 50, 2004.)