Continuous-time random walks on a long-range hierarchical model

We present the autocorrelation function $P_0$(t) and the mean number of visited sites S(t) for continuous-time random walks on a new hierarchical model proposed by Knapp. With broad waiting-time distributions ψ(t)∼$t^{\mathrm{-}\alpha \mathrm{-}1}$ we find S(t)∼$t^{\alpha \gamma }$ (subordination) and S(t)∼1/$P_0$(t) (compact exploration) for small temperatures, where γ characterizes the energetic disorder. These results parallel our findings for random walks on ultrametric spaces and on fractals.