On the effective medium theory of random linear networks

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Abstract
The author studies the effective medium approximation for uncorrelated random linear networks. For various probability distributions of conductance compares the effective medium average value to the direct numerical average and study the magnitude of the correction terms by a mixture of analytical and numerical arguments. He argues that for all 'non-critical' conductance distributions-for systems not dominated by very low values of conductance and not near the conduction threshold-the effective medium approximation is quite accurate, with errors of order 1%. For any conduction distribution, effective medium theory is shown to be exact in the two limits of coordination number sigma =2 and sigma to infinity . Some remarks on the critical path approximation are presented.