On the Ornstein-Zernike behaviour for the Bernoulli bond percolation on $\mathbb{Z}^{d},d\geq3,$ in the supercitical regime

Details On the Ornstein-Zernike behaviour for the Bernoulli bond percolation on $\mathbb{Z}^{d},d\geq3,$ in the supercitical regime On the Ornstein-Zernike behaviour for the Bernoulli bond percolation on $\mathbb{Z}^{d},d\geq3,$ in the supercitical regime

2011-04-08

arxiv.org/abs/1104.1595v2

Mathematics

Probability

18 pages, published version

Scientific paper

10.1007/s10955-011-0330-8

We prove Ornstein-Zernike behaviour in every direction for finite connection
functions of bond percolation on $\mathbb{Z}^{d}$ for $d\geq3$ 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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