Limit distributions in random resistor networks

Rafael F. Angulo and Ernesto Medina

Physica A: Statistical Mechanics and its Applications, 1992, vol. 191, issue 1, 410-414

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.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:191:y:1992:i:1:p:410-414

DOI: 10.1016/0378-4371(92)90559-9

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