My research project is concerned with the study of the statistics of nonlinear systems. Our main interest is in using the double lenses of Wave Turbulence Theory and the Functional Renormalisation Group to gauge the average out-of-equilibrium behaviour of complex systems, beyond the perturbative expansions leading to the Wave Kinetic Equation. We are interested both in the study of theoretical toy models, like the Majda-Mclaughling-Tabak model, and physically relevant nonlinear PDE, like the shallow water and Gross-Pitaevskii equations.