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Scaling relations for 2D-percolation

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Abstract

We prove that the relations 2D-percolation hold for the usual critical exponents for 2D-percolation, provided the exponents δ andv exist. Even without the last assumption various relations (inequalities) are obtained for the singular behavior near the critical point of the correlation length, the percolation probability, and the average cluster size. We show that in our models the above critical exponents have the same value for approach ofp to the critical probability from above and from below.

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Authors and Affiliations

  1. Department of Mathematics, Cornell University, 14853, Ithaca, NY, USA

    Harry Kesten

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  1. Harry Kesten
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Communicated by M. E. Fisher

Research supported by the NSF through grants to Cornell University and to the Institute for Mathematics and its Applications, Minneapolis

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Kesten, H. Scaling relations for 2D-percolation. Commun.Math. Phys. 109, 109–156 (1987). https://doi.org/10.1007/BF01205674

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  • DOI: https://doi.org/10.1007/BF01205674

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