Global first-passage times of fractal lattices.

The global first passage time density of a network is the probability that a random walker released at a random site arrives at an absorbing trap at time T . We find simple expressions for the mean global first passage time <T> for five fractals: the d-dimensional Sierpinski gasket, T fractal, hierarchical percolation model, Mandelbrot-Given curve, and a deterministic tree. We also find an exact expression for the second moment <T(2)> and show that the variance of the first passage time, Var(T) , scales with the number of nodes within the fractal N such that Var(T) approximately N(4/d[over]), where d[over] is the spectral dimension.