We prove Ornstein-Zernike behaviour in every direction for finite connection functions of bond percolation on a"currency sign (d) for da parts per thousand yen3 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.

On the Ornstein-Zernike Behaviour for the Bernoulli Bond Percolation on Z(d), d >= 3, in the Supercritical Regime

GIANFELICE, Michele
2011

Abstract

We prove Ornstein-Zernike behaviour in every direction for finite connection functions of bond percolation on a"currency sign (d) for da parts per thousand yen3 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.
Percolation; Local limit teorem; Decay of connectivities; Multidimesional renewal process
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11770/159308
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