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

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.