Global first passage times on fractal lattices

C. P. Haynes; A. P. Roberts

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arXiv · 0809.0563

Global first passage times on fractal lattices

C. P. Haynes·A. P. Roberts

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Abstract

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 for five fractals. We also find an exact expression for the second moment 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) ~ N^(4/\bar{d}), where \bar{d} is the spectral dimension.

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C. P. Haynes, A. P. Roberts. 2008-09-03. Global first passage times on fractal lattices. https://arxiv.org/abs/0809.0563

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