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April 2002 Ornstein-Zernike theory for the Bernoulli bond percolation on $\mathbb{Z}^d$
Massimo Campanino, Dmitry Ioffe
Ann. Probab. 30(2): 652-682 (April 2002). DOI: 10.1214/aop/1023481005

Abstract

We derive a precise Ornstein–Zernike asymptotic formula for the decay of the two-point function $\mathbb{P}_p (0 \leftrightarrow x)$ of the Bernoulli bond percolation on the integer lattice $\mathbb{Z}^d$ in any dimension $d \geq 2$, in any direction $x$ and for any subcritical value of $p < p_c (d)$.

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Massimo Campanino. Dmitry Ioffe. "Ornstein-Zernike theory for the Bernoulli bond percolation on $\mathbb{Z}^d$." Ann. Probab. 30 (2) 652 - 682, April 2002. https://doi.org/10.1214/aop/1023481005

Information

Published: April 2002
First available in Project Euclid: 7 June 2002

zbMATH: 1013.60077
MathSciNet: MR1905854
Digital Object Identifier: 10.1214/aop/1023481005

Subjects:
Primary: 60F15 , 60K15 , 60K35 , 82A43

Keywords: Local limit theorems , multidimensional renewal , Ornstein-Zernike decay of connectivities , percolation , renormalization

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.30 • No. 2 • April 2002
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