On a universality class of anomalous diffusion

We show that when transport is asymptotically dominated by ballistic excursions the momentsof displacement exhibit a universal behaviour, and their values that can be obtained after an appropriate rescaling of the mean square displacement in terms of the asymptotic behaviour of a minimal transport model that be call Fly-and-Die. Furthermore, we show that this universality extends to the displacement correlation function. We obtain the statistical properties defining a universality class to which the details and nature of the dynamics are irrelevant. We support this by studying several models exhibiting strong anomalous diffusion.