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Large scale properties of the IIIC for 2D percolation

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  • Chayes, L.
  • Nolin, P.

Abstract

We reinvestigate the 2D problem of the inhomogeneous incipient infinite cluster where, in an independent percolation model, the density decays to pc with an inverse power, [lambda], of the distance to the origin. Assuming the existence of critical exponents (as is known in the case of the triangular site lattice) if the power is less than 1/[nu], with [nu] the correlation length exponent, we demonstrate an infinite cluster with scale dimension given by DH=2-[beta][lambda]. Further, we investigate the critical case [lambda]c=1/[nu] and show that iterated logarithmic corrections will tip the balance between the possibility and impossibility of an infinite cluster.

Suggested Citation

  • Chayes, L. & Nolin, P., 2009. "Large scale properties of the IIIC for 2D percolation," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 882-896, March.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:3:p:882-896
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