Renormalization-group Approach To Dynamic Properties of Hierarchical Networks

Diffusion processes in the presence of hierarchical distributions of transition rates or waiting times are investigated by Renormalization Group (RG) techniques. Diffusion on one-dimensional chains, loop-less fractals and fully ultrametric spaces are considered. RG techniques are shown to be most natural and powerful to apply when infinitely many time scales are simultaneously involved in a problem. Generalizations and extensions of existing models and results are easily accomplished in the RG context. Wherever possible, heuristic scaling arguments are also presented in order to give an easier physical interpretation of the analytical results. Two relevant applications of ultradiffusion models are reviewed in detail. One of them concerns breakdown of dynamic scaling in a one-dimensional hierarchical Glauber chain. The other one is in the context of tethered random surface models.