Effective target arrangement in a deterministic scale-free graph

Details Effective target arrangement in a deterministic scale-free graph Effective target arrangement in a deterministic scale-free graph

2010-03-17

arxiv.org/abs/1003.3359v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, 5 figures

Scientific paper

We study the random walk problem on a deterministic scale-free network, in the presence of a set of static, identical targets; due to the strong inhomogeneity of the underlying structure the mean first-passage time (MFPT), meant as a measure of transport efficiency, is expected to depend sensitively on the position of targets. We consider several spatial arrangements for targets and we calculate, mainly rigorously, the related MFPT, where the average is taken over all possible starting points and over all possible paths. For all the cases studied, the MFPT asymptotically scales like N^{theta}, being N the volume of the substrate and theta ranging from (1 - log 2/log3), for central target(s), to 1, for a single peripheral target.

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