Large Deviations for Ablowitz-Ladik lattice, and the Schur flow

Abstract

We consider the Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, and the Schur flow. We derive large deviations principles for the distribution of the empirical measures of the equilibrium measures for these ensembles. As a consequence, we deduce their almost sure convergence. Moreover, we are able to characterize their limit in terms of the equilibrium measure of the Circular, and the Jacobi beta ensemble respectively.

28 pages

References in corpus (3)

• The collision rate ansatz for the classical Toda lattice
• Hydrodynamic equations for the Ablowitz-Ladik discretization of the nonlinear Schroedinger equation
• Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, Circular $\beta$-ensemble and double confluent Heun equation

Cited by in corpus (6)

• Equilibrium Spacetime Correlations of the Toda Lattice on the Hydrodynamic Scale
• Discrete integrable systems and random Lax matrices
• Particle Scattering and Fusion for the Ablowitz-Ladik Chain
• CLT for real beta-ensembles at high temperature
• Generalized Hydrodynamics for the Volterra lattice: Ballistic and nonballistic behavior of correlation functions
• Lax random matrices from Calogero systems