We will study integrable equations of KdV and NLS type with random initial data. We will consider a Gibbs ensemble of probability measures in the physical space and study the behaviour of correlators and fluctuations over large times. Since we consider integrable PDEs that can be integrated via inverse scattering, very detailed information of statistical quantities over large times will be derived.

• Alexander Bufetov (CNRS, Aix-Marseille Université)
• Tamara Grava (SISSA Trieste, Bristol University & Aix-Marseille Université)
• Mattia Cafasso (Université d’Angers)
• Ken McLaughlin (Colorado State University)
• Peter Miller (University of Michigan, Ann Arbor)