CMV matrices in random matrix theory and integrable systems: a survey

Abstract

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.

Based on a talk given at the Short Program on Random Matrices, Random Processes and Integrable Systems, CRM, Universite de Montreal, 2005

Cited by in corpus (6)

• Local Conservation Laws and the Hamiltonian Formalism for the Ablowitz-Ladik Hierarchy
• Hydrodynamic equations for the Ablowitz-Ladik discretization of the nonlinear Schroedinger equation
• Algebro-Geometric Finite-Gap Solutions of the Ablowitz-Ladik Hierarchy
• Multiple phases and meromorphic deformations of unitary matrix models
• The CMV bispectral problem
• The Ablowitz-Ladik Hierarchy Revisited