Constrained spin-dynamics description of random walks on hierarchical scale-free networks

The random walk problem on hierarchical scale-free networks was discussed. The random walk problem was mapped onto a dynamical Ising spin chain system in one dimensional. It was analyzed that the characteristic relaxation time scale grew algebraically. It was found that the origin of the power-law saling behavior of the relaxation time and the autocorrelation functions was on the tree structure of the spin configuration space.