Exact calculations of first-passage quantities on recursive networks.

Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Case Courrier 121, Université Paris 6, 4 Place Jussieu, FR-75255 Paris Cedex, France.
Physical Review E (Impact Factor: 2.31). 02/2012; 85(2 Pt 2):026113. DOI: 10.1103/PhysRevE.85.026113
Source: PubMed

ABSTRACT 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 in characterizing transport in complex media. We explicitly perform calculations for different classes of recursive networks [finitely ramified fractals, scale-free (trans)fractals, nonfractals, mixtures between fractals and nonfractals, nondecimable hierarchical graphs] of arbitrary size. Our approach unifies and significantly extends the available results in the field.

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