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Limit distributions in random resistor networks

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  • Angulo, Rafael F.
  • Medina, Ernesto

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.

Suggested Citation

  • Angulo, Rafael F. & Medina, Ernesto, 1992. "Limit distributions in random resistor networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 410-414.
    • Handle: RePEc:eee:phsmap:v:191:y:1992:i:1:p:410-414
    DOI: 10.1016/0378-4371(92)90559-9
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