Spectral dimensions and first passage time distribution of hierarchical scale-free networks

초록

The spectral dimension has been widely used to understand transport properties on regular and fractal lattices. Also, the mean rst passage time of random walk is another quantity which provides the key information of the dynamics. Under some scaling arguments, it can be shown that the two quantities are closely related. Here we study the spectral dimension and the rst passage time distribution of random walks on hierarchical scale-free networks and con rm the scaling arguments. Applying the continuum to discrete transformations, we obtain the generating function of global first passage time(GFPT) distribution exactly. From the result, the asymptotic behavior of higher moments of GFPT is drawn to decide the spectral dimension. We also compare the result with the previous result, which is directly calculated via the renormalization group approach, and con rm the scaling arguments. The analytic results are con rmed by simulation results and their implications for the architecture of complex systems are discussed.