Distribution of the logarithms of currents in percolating resistor networks. I. Theory

The distribution of currents, i b , in the bonds b of a randomly diluted resistor network at the percolation threshold is investigated through a study of the moments of the distribution P(i 2 ) and the moments of the distribution P(γ), where γ=-lni b 2 . For q>q, the qth moment of P(i 2 ), M q (i.e., the average of i 2q ), scales as a power law of the system size L, with a multifractal (noise) exponent ψ(q)-ψ(0). Numerical data indicate that q c is negative, but becomes small for large L