A quantitative analysis of resistor networks with logarithmically wide distribution of conductances

We use a percolation analysis to study the conductivity of a random resistor network with bond conductances gi = g0 exp(λxi), where xi is a random variable. In the limit λ → ∞ we may write the network conductivity as σ = ca2−dgcλ−y where a is the lattice constant, y a critical exponent, c a constant, and gc the percolation conductance. We derive rigorous bounds to σ and we present evidence that supports the hypothesis that y = 0 for all 2D lattices.