Large scale properties of the IIIC for 2D percolation |
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Authors: | L. Chayes P. Nolin |
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Affiliation: | 1. Department of Mathematics, UCLA, Los Angeles, CA 90059-1555, USA;2. Département de Mathématiques et Applications, ENS, 75230 Paris cedex 05, France;3. Laboratoire de Mathématiques, Université Paris-Sud, 91405 Orsay cedex, France |
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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, λ, 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/ν, with ν the correlation length exponent, we demonstrate an infinite cluster with scale dimension given by DH=2−βλ. Further, we investigate the critical case λc=1/ν and show that iterated logarithmic corrections will tip the balance between the possibility and impossibility of an infinite cluster. |
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Keywords: | 60K35 82B43 |
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