A connection between linear and nonlinear resistor networks

The authors explore the connection between the higher moments of the current (or voltage) distribution in a random linear resistor network, and the resistance of a nonlinear random resistor network. They find that the two problems are very similar, and that an infinite set of exponents are required to fully characterise each problem. These exponent sets are shown to be identical on a particular hierarchical lattice, a simple model which accurately describes the geometrical properties of the backbone of the infinite cluster at the percolation threshold and also the voltage distribution on this structure.