Herbert Spohn – Technical University Munich
Wednesday, April 16th , 10:45AM DST
Random matrix theory and integrable many-particle systems
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, in which case the Lax matrix is close to a GUE type random matrix , while for the Ablowitz-Ladik chain one arrives at a CUE random matrix. For the Toda chain, much studied are localized deviations from a periodic background configuration. We will also discuss the resulting random matrix structure.