We aim here at showing how the equilibrium measures for a finite network can be used to obtain simple expressions for both Green and Poisson kernels and hence we can deduce nice expressions of the hitting time and the effective resistance. Also, we will give a new and simple proof, using equilibrium measures, of the algorithm that compute the resistive inverse of a effective resistance matrix.
Carmona, A., Bendito, E., Encinas, A. Equilibrium measures on finite networks. Effective resistance and hitting time. "Electronic notes in discrete mathematics", 2001, vol. 10, p. 68-71.