Communications in Mathematical Physics

, Volume 105, Issue 1, pp 133–152 | Cite as

Bulk transport properties and exponent inequalities for random resistor and flow networks

  • J. T. Chayes
  • L. Chayes


The properties of random resistor and flow networks are studied as a function of the density,p, of bonds which permit transport. It is shown that percolation is sufficient for bulk transport, in the sense that the conductivity and flow capacity are bounded away from zero wheneverp exceeds an appropriately defined percolation threshold. Relations between the transport coefficients and quantities in ordinary percolation are also derived. Assuming critical scaling, these relations imply upper and lower bounds on the conductivity and flow exponents in terms of percolation exponents. The conductivity exponent upper bound so derived saturates in mean field theory.


Neural Network Statistical Physic Field Theory Complex System Lower Bound 
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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • J. T. Chayes
    • 1
  • L. Chayes
    • 1
  1. 1.Laboratory of Atomic and Solid State Physics, Clark HallCornell UniversityIthacaUSA

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