Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2012-02-22
Phys. Rev. E 85, 026113 (2012)
Physics
Condensed Matter
Statistical Mechanics
16 pages, 10 figures
Scientific paper
We present general methods to exactly calculate mean-first passage quantities on self-similar networks defined recursively. In particular, we calculate the mean first-passage time and the splitting probabilities associated to a source and one or several targets; averaged quantities over a given set of sources (e.g., same-connectivity nodes) are also derived. The exact estimate of such quantities highlights the dependency of first-passage processes with respect to the source-target distance, which has recently revealed to be a key parameter to characterize transport in complex media. We explicitly perform calculations for different classes of recursive networks (finitely ramified fractals, scale-free (trans)fractals, non-fractals, mixtures between fractals and non-fractals, non-decimable hierarchical graphs) of arbitrary size. Our approach unifies and significantly extends the available results in the field.
Agliari Elena
Benichou Olivier
Meyer Bertrand
Voituriez Raphael
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