Global first-passage times of fractal lattices

Haynes, C. P. and Roberts, A. P. (2008) Global first-passage times of fractal lattices. Physical Review E, 78 4: 041111-1-041111-9. doi:10.1103/PhysRevE.78.041111

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Author Haynes, C. P.
Roberts, A. P.
Title Global first-passage times of fractal lattices
Journal name Physical Review E   Check publisher's open access policy
ISSN 1539-3755
Publication date 2008-10-10
Year available 2008
Sub-type Article (original research)
DOI 10.1103/PhysRevE.78.041111
Open Access Status File (Publisher version)
Volume 78
Issue 4
Start page 041111-1
End page 041111-9
Total pages 9
Place of publication New York, U.S.A
Publisher American Physical Society
Language eng
Subject C1
970101 Expanding Knowledge in the Mathematical Sciences
019999 Mathematical Sciences not elsewhere classified
0101 Pure Mathematics
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 < 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)similar to N(4/d), where d is the spectral dimension.
Formatted 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 < 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)similar to N-4/d, where d is the spectral dimension.
Keyword Fractals
Percolation
Probability
Random processes
Trees (mathematics)
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: 2009 Higher Education Research Data Collection
School of Mathematics and Physics
School of Physical Sciences Publications
 
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Citation counts: TR Web of Science Citation Count  Cited 53 times in Thomson Reuters Web of Science Article | Citations
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Created: Fri, 27 Mar 2009, 19:50:17 EST by Marie Grove on behalf of School of Mathematics & Physics