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December  2004, 3(4): 581-606. doi: 10.3934/cpaa.2004.3.581

Ornstein-Zernike behavior for the Bernoulli bond percolation on $\mathbb Z^d$ in the supercritical regime

G. A. Braga 1, , A. Procacci 2, and  R. Sanchis 2,

1. 

Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 1621, Belo Horizonte, 30161-970, Brazil
2. 

Department of Mathematics, Universidade Federal de Minas Gerais, 30161-970 Belo Horizonte, Brazil, Brazil

Received  November 2003 Revised  May 2004 Published  September 2004

We derive an Ornstein-Zernike asymptotic formula for the decay of the two point finite connectivity function $\phi^f_p(x\leftrightarrow y)$ of the Bernoulli bond percolation process on $\mathbb Z^d$, in the supercritical phase, along the principal directions, for $d\ge 3$, and for values of $p$ sufficiently near to $p=1$.
Keywords: Ornstein Zernike behavior., cluster expansion, Percolation.
Mathematics Subject Classification: 60K35.
Citation: G. A. Braga, A. Procacci, R. Sanchis. Ornstein-Zernike behavior for the Bernoulli bond percolation on $\mathbb Z^d$ in the supercritical regime. Communications on Pure and Applied Analysis, 2004, 3 (4) : 581-606. doi: 10.3934/cpaa.2004.3.581
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