Mathematical Physics Seminar

We construct an ensemble of (sparse) random matrices whose eigenvalues follow the Gibbs distribution for n particles of Coulomb gas on the unit circle at any given inverse temperature. 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.