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 $p < p_c (d)$.
Publié le : 2002-04-14
Classification:
percolation,
Ornstein-Zernike decay of connectivities,
multidimensional renewal,
renormalization,
local limit theorems,
60F15,
60K15,
60K35,
82A43
@article{1023481005,
author = {Campanino, Massimo and Ioffe, Dmitry},
title = {Ornstein-Zernike theory for the Bernoulli bond percolation on
$\mathbb{Z}^d$},
journal = {Ann. Probab.},
volume = {30},
number = {1},
year = {2002},
pages = { 652-682},
language = {en},
url = {http://dml.mathdoc.fr/item/1023481005}
}
Campanino, Massimo; Ioffe, Dmitry. Ornstein-Zernike theory for the Bernoulli bond percolation on
$\mathbb{Z}^d$. Ann. Probab., Tome 30 (2002) no. 1, pp. 652-682. http://gdmltest.u-ga.fr/item/1023481005/