The two-dimensional stochastic Burgers equation is critical under diffusive scaling, so standard singular-SPDE solution theories do not apply. This concept covers the proof that it is only logarithmically superdiffusive, with diffusion coefficient growing like (log t)^{2/3} and a coupling-constant prefactor matching the one-dimensional KPZ equation, and the associated superdiffusive central limit theorem identifying an explicit Gaussian renormalization-group fixed point via resolvent control of the equation's generator.
The Stochastic Burgers Equation (SBE) is a singular nonlinear stochastic PDE modeling the fluctuations, on mesoscopic scales, of driven diffusive systems with one conserved scalar. In spatial dimensi…