On the Ornstein-Zernike behaviour for the Bernoulli bond percolation on ${\mathbb{Z}}^d,d\ge 3,$ in the supercitical regime

Abstract

We prove Ornstein-Zernike behaviour in every direction for finite connection functions of bond percolation on ${\mathbb{Z}}^d$ for $d\ge 3$ 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.

18 pages, published version

References in corpus (1)

• Ornstein-Zernike Theory for the finite range Ising models above T_c

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