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

Abstract

We demonstrate that the source to target mean first passage time (MFPT) is approximately given by the potential difference of an electrostatic problem which shows that the MFPT scales like the resistance between the target and a distant shell. This analogy allows the asymmetry of the MFPT on non uniform lattices to be incorporated and provides a number of useful insights. For example, on transient lattices, the MFPT converges exactly to the product of the mass and the site dependent resistance between the target and a shell at infinity.