Workshop: Random matrix theory and integrable many-particle systems

Speaker
Spohn, Technical University Munich

Abstract
In our context integrable systems are characterized by possessing a Lax matrix. If the initial data are random, so is the Lax matrix. We will illustrate this structure for the Toda lattice, which is close to GUE, and  for the Ablowitz-Ladik chain, which is close to CUE. For the Toda chain, much studied are deviations from a standing still perfectly periodic configuration. We will discuss the resulting random matrix problems.