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

TL;DR

This paper introduces an electrostatic analogy to approximate the source-to-target mean first passage time (MFPT) on lattices, revealing how MFPT scales with resistance and providing insights into asymmetry and convergence properties.

Contribution

It presents a novel electrostatic approximation for MFPT on lattices, incorporating asymmetry and convergence behavior in non-uniform and transient lattices.

Findings

MFPT approximates potential difference in electrostatic problems

MFPT scales with resistance between target and distant shell

On transient lattices, MFPT converges to resistance times mass

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.