Limit distributions in random resistor networks

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Abstract

The question of attraction to stable limit distributions in random resistor networks (RRNs) is explored numerically. Transport in networks with power law distributions of conductances of the form P(g) = |μ|gμ−1 are considered. Distributions of equivalent conductances are estimated on hierarchical lattices as a function of size L and the parameter μ. We find that only lattices at the percolation threshold can support transport in a Levy-like basin. For networks above the percolation threshold, convergence to a Gaussian basin is always the case, and a disorder length ξD is identified, beyond which the system is effectively homogeneous. This length scale diverges, when the microscopic distribution of conductors is exponentially wide (μ→0), as ξD∼|μ|−1.6−0.1.

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