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.Comment: 28 page
