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On the Ornstein-Zernike Behaviour for the Bernoulli Bond Percolation on \(\pmb{\mathbb{Z}}^{d},d\geq3\), in the Supercritical Regime

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Abstract

We prove Ornstein-Zernike behaviour in every direction for finite connection functions of bond percolation on ℤd for d≥3 when p, the probability of occupation of a bond, is sufficiently close to 1. Moreover, we prove that equi-decay surfaces are locally analytic, strictly convex, with positive Gaussian curvature.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Bologna, P.zza di Porta San Donato, 5, 40127, Bologna, Italy

    M. Campanino

  2. Dipartimento di Matematica, Università della Calabria, Campus di Arcavacata, Ponte P. Bucci, cubo 30B, 87036, Arcavacata di Rende, Italy

    M. Gianfelice

Authors
  1. M. Campanino
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  2. M. Gianfelice
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Correspondence to M. Campanino.

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Campanino, M., Gianfelice, M. On the Ornstein-Zernike Behaviour for the Bernoulli Bond Percolation on \(\pmb{\mathbb{Z}}^{d},d\geq3\), in the Supercritical Regime. J Stat Phys 145, 1407–1422 (2011). https://doi.org/10.1007/s10955-011-0330-8

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  • DOI: https://doi.org/10.1007/s10955-011-0330-8

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