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Electrostatic approximation of source-to-target mean first-passage times on networks

Anthony P. Roberts1 and Christophe P. Haynes1,2

  • 1School of Mathematics and Physics, University of Queensland, Brisbane 4072, Australia
  • 2CEA, DAM, DIF, F-91297 Arpajon, France

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Phys. Rev. E 83, 031113 – Published 15 March, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.031113

Abstract

We show that the distance dependence of the source-to-target mean-first-passage time (MFPT) on a finite network with M links is approximately given by 2M times the target-to-shell resistance. For networks on which a random walker is transient the long-range MFPT is well approximated by the site-dependent resistance from the target to infinity. The result extends a recent scaling result for the MFPT to site-inhomogeneous lattices where the MFPT depends on the location of the source and targets and can be highly source-target asymmetric.

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Phys. Rev. E 83, 031113– Published 15 March, 2011
  • Received 19 October 2010

©2011 American Physical Society

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