Dynamics of Non-Gaussian Hydrodynamic Fluctuations

In the context of the search for the QCD critical point we present dynamical evolution equations for Non-Gaussian fluctuations in hydrodynamics. We introduce a novel generalization of the Wigner transform to multi-point correlators and derive the evolution equations for three- and four-point Wigner functions for the problem of nonlinear stochastic diffusion with multiplicative noise. The formalism and the results we present are very general and would pertain to problems where non- linearity and non-Gaussian fluctuations are of interest.