The theory of random matrices plays an important role in many areas of pure mathematics
and employs a variety of sophisticated mathematical tools (analytical, probabilistic and …

CMV matrices: Five years after - ScienceDirect Skip to main contentSkip to article Elsevier logo
Journals & Books Search RegisterSign in View PDF Download full issue Search ScienceDirect …

The lecture notes cover the emergence of generalized hydrodynamics for the classical and
quantum Toda chain, the classical Calogero fluid, the Ablowitz-Ladik discretization of the …

Ablowitz and Ladik discovered a discretization that preserves the integrability of the
nonlinear Schrödinger equation in one dimension. We compute the generalized free energy …

We consider the discrete defocusing nonlinear Schrödinger equation in its integrable
version, which is called defocusing Ablowitz–Ladik lattice. We consider periodic boundary …

The purpose of the present paper is to establish moderate deviation principles for a rather
general class of random variables fulfilling certain bounds of the cumulants. We apply a …

Matrix orthogonal Laurent polynomials in the unit circle and the theory of Toda-like
integrable systems are connected using the Gauss–Borel factorization of two, left and a right …

Abstract We consider the Generalized Gibbs ensembles of the Ablowitz-Ladik lattice and of
the Schur flow. We derive large deviations principles for the distribution of the empirical …

Nenciu and Simon found that the analogue of the Toda system in the context of orthogonal
polynomials on the unit circle is the defocusing Ablowitz-Ladik system. In this paper we use …

Using the spectral theory of unitary operators and the theory of orthogonal polynomials on
the unit circle, we propose a simple matrix model for the following circular analog of the …