The Annals of Probability

Ornstein-Zernike theory for the Bernoulli bond percolation on $\mathbb{Z}^d$

Massimo Campanino and Dmitry Ioffe

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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 $p < p_c (d)$.

Article information

Source
Ann. Probab., Volume 30, Number 2 (2002), 652-682.

Dates
First available in Project Euclid: 7 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1023481005

Digital Object Identifier
doi:10.1214/aop/1023481005

Mathematical Reviews number (MathSciNet)
MR1905854

Zentralblatt MATH identifier
1013.60077

Subjects
Primary: 60F15: Strong theorems 60K15: Markov renewal processes, semi-Markov processes 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82A43

Keywords
percolation Ornstein-Zernike decay of connectivities multidimensional renewal renormalization local limit theorems

Citation

Campanino, Massimo; Ioffe, Dmitry. Ornstein-Zernike theory for the Bernoulli bond percolation on $\mathbb{Z}^d$. Ann. Probab. 30 (2002), no. 2, 652--682. doi:10.1214/aop/1023481005. https://projecteuclid.org/euclid.aop/1023481005


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References

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