We prove Ornstein-Zernike behaviour in every direction for finite connection functions of bond percolation on $pmb{mathbb{Z}}^{d}$ for $dgeq3$, when $p$, the probability of occupation of a bond, is sufficiently close to $1$. Moredover we prove that the equi-decay surfaces are locally analytic, strictly positive, with positive Gaussian curvature.
M. Campanino, M. Gianfelice (2011). On the Ornstein-Zernike Behaviour for the Bernoulli Bond Percolation on $pmb{mathbb{Z}}^{d},dgeq3$, in the Supercritical Regime. JOURNAL OF STATISTICAL PHYSICS, 145, 1407-1422 [10.1007/s10955-011-0330-8].
On the Ornstein-Zernike Behaviour for the Bernoulli Bond Percolation on $pmb{mathbb{Z}}^{d},dgeq3$, in the Supercritical Regime
CAMPANINO, MASSIMO;
2011
Abstract
We prove Ornstein-Zernike behaviour in every direction for finite connection functions of bond percolation on $pmb{mathbb{Z}}^{d}$ for $dgeq3$, when $p$, the probability of occupation of a bond, is sufficiently close to $1$. Moredover we prove that the equi-decay surfaces are locally analytic, strictly positive, with positive Gaussian curvature.File in questo prodotto:
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