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.)