Potential Theory on Finite Networks

We survey here some techniques from Potential Theory and show their use in electrical networks. We are focused on the linear aspect of the theory; that is, on the analysis of singular an positive semidefinite Schrödinger operators and we show the relation between this class of operators and singular M-matrices, paying attention on the properties of superharmonic functions. We also apply these methods to establish some global results on the associated Markov chains.