Ornstein-Zernike theory for the Bernoulli bond percolation on \(\mathbb Z^d\). (English) Zbl 1013.60077

Summary: 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 \(p<p_c(d)\).


60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F15 Strong limit theorems
60K15 Markov renewal processes, semi-Markov processes
82B43 Percolation
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