5 research outputs found
Matrix models for circular ensembles
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
CMV matrices in random matrix theory and integrable systems: a survey
We present a survey of recent results concerning a remarkable class of
unitary matrices, the CMV matrices. We are particularly interested in the role
they play in the theory of random matrices and integrable systems. Throughout
the paper we also emphasize the analogies and connections to Jacobi matrices.Comment: Based on a talk given at the Short Program on Random Matrices, Random
Processes and Integrable Systems, CRM, Universite de Montreal, 200