Linear and anomalous front propagation in systems with non-Gaussian diffusion: The importance of tails

We investigate front propagation in systems with diffusive and subdiffusive behavior. The scaling behavior ofmoments of the diffusive problem, both in the standard and in the anomalous cases, is not enough to determine thefeatures of the reactive front. In fact, the shape of the bulk of the probability distribution of the transport process,which determines the diffusive properties, is important just for preasymptotic behavior of front propagation, whilethe precise shape of the tails of the probability distribution determines asymptotic behavior of front propagation