Current distribution in random resistor networks

The de Arcangelis Redner Coniglio hierarchical model for a random resistor network implies a log-binomial current distribution. Simulations show that small currents are more abundant than this. It is shown here that the invariance of the current distribution with respect to the direction of the applied field implies a different form which is in better qualitative agreement with simulations, and which is correct in the high-dimensionality limit. It is generally shown that the negative moments of the current distribution do not exist. Two-dimensional simulations seem to have a scaling form different from the multifractal scaling law.