Mathematics

We shall present recent developments in the justification of macroscopic laws of statistical physics in the context of interacting waves. The key mathematical problem is the rigorous justification of a kinetic equation which describes the average evolution of the system starting from Hamiltonian first principles. In this talk, we carry out this program for the wave-system given by the cubic Schrödinger equation, with a stochastic forcing and viscous dissipation, by combining tools from probability, combinatorics and harmonic analysis. We will describe various regimes depending on the relative strength of the dissipation and the nonlinear interactions, which give rise to different kinetic equations. Based on joint work with Zaher Hani.