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Haynes CP, Roberts AP. Global first-passage times of fractal lattices. Phys Rev E Stat Nonlin Soft Matter Phys. 2008;78(4):041111doi: 10.1103/PhysRevE.78.041111.
Haynes, C. P., & Roberts, A. P. (2008). Global first-passage times of fractal lattices. Physical review. E, Statistical, nonlinear, and soft matter physics, 78(4), 041111. https://doi.org/10.1103/PhysRevE.78.041111
Haynes, C P, and Roberts, A P. "Global first-passage times of fractal lattices." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 78,4 (2008): 041111. doi: https://doi.org/10.1103/PhysRevE.78.041111
Haynes CP, Roberts AP. Global first-passage times of fractal lattices. Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Oct;78(4):041111. doi: 10.1103/PhysRevE.78.041111. Epub 2008 Oct 10. PMID: 18999383.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Oct;78(4):041111. doi: 10.1103/PhysRevE.78.041111. Epub 2008 Oct 10.

Global first-passage times of fractal lattices.

Physical review. E, Statistical, nonlinear, and soft matter physics

C P Haynes, A P Roberts

Affiliations

  1. School of Physical Sciences, University of Queensland, Queensland 4072, Australia.

PMID: 18999383 DOI: 10.1103/PhysRevE.78.041111

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: 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 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.

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