Superdiffusive central limit theorem for a Brownian particle in a critically-correlated incompressible random drift

We consider the long-time behavior of a diffusion process on $\mathbb{R}^d$ advected by a stationary random vector field which is assumed to be divergence-free, dihedrally symmetric in law and have a log-correlated potential. A special case includes $\nabla^\perp$ of the Gaussian free field in two d