Anomalous voltage distribution of random resistor networks and a new model for the backbone at the percolation threshold

Abstract

We develop a new approach for studying the random resistor network by focusing on the distribution of voltage drops across each bond We introduce a simple model which provides a useful description of the percolating backbone, and which shows that the voltage distribution is log normal, with an infinite set of exponents required to describe the voltage moments. This latter prediction is verified by simulations of a resistor network on the square lattice.