Current distribution in systems with anomalous diffusion: renormalisation group approach

We investigate the asymptotic properties of the large deviation function of the integrated particle current in systems, in or out of thermal equilibrium, whose dynamics exhibits anomalous diffusion. The physical systems covered by our study include mutually repelling particles with a drift, a driven lattice gas displaying a continuous nonequilibrium phase transition, and particles diffusing in a anisotropic random advective field. It is exemplified how renormalisation group techniques allow for a systematic determination of power laws in the corresponding current large deviation functions. We show that the latter are governed by known universal scaling exponents, specifically, the anomalous dimension of the noise correlators.