Ornstein-Zernike theory for the Bernoulli bond percolation on ℤd

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Abstract

We derive a precise Ornstein-Zernike asymptotic formula for the decay of the two-point function ℙp(0 ↔ x) of the Bernoulli bond percolation on the integer lattice ℤd in any dimension d ≥ 2, in any direction x and for any subcritical value of p < pc(d).

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Campanino, M., & Ioffe, D. (2002). Ornstein-Zernike theory for the Bernoulli bond percolation on ℤd. Annals of Probability, 30(2), 652–682. https://doi.org/10.1214/aop/1023481005

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