Irina Nenciu

MATRIX MODELS FOR CIRCULAR ENSEMBLES

The Gibbs distribution for n particles of the Coulomb gas on the unit circle at inverse temperature β is given by

Lax pairs for the Ablowitz-Ladik system via orthogonal polynomialson the unit circle

We investigate the existence and properties of an integrable system related to orthogonal polynomials on the unit circle. We prove that the main evolution of the system is defocusing Ablowitz-Ladik (also known as the integrable discrete nonlinear Schroedinger equation). In particular, we give a new proof of complete integrability for this system. Furthermore, we use the CMV and extended CMV matrices defined in the context of orthogonal polynomials on the unit circle by Cantero, Moral, and Velazquez, and Simon, respectively, to construct Lax pair representations for the Ablowitz-Ladik hierarchy in the periodic, finite, and infinite settings.

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.

On Confining Potentials and Essential Self-Adjointness for Schrödinger Operators on Bounded Domains in {\mathbb{R}}^n

Abstract.Let Ω be a bounded domain in

On Essential Self-Adjointness for Magnetic Schrödinger and Pauli Operators on the Unit Disc in {\mathbb {R}^2}

{\mathbb{R}}^n

CMV : The unitary analogue of jacobi matrices

with C2-smooth boundary,

The periodic defocusing Ablowitz–Ladik equation and the geometry of Floquet CMV matrices

\partial \Omega