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

DOI10.1214/aop/1023481005zbMath1013.60077OpenAlexW2045291455MaRDI QIDQ1872273

Dimitry Ioffe, Massimo Campanino

Publication date: 6 May 2003

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1023481005

zbMATH Keywords

percolationrenormalizationlocal limit theoremsmultidimensional renewalOrnstein-Zernike decay of connectivities

Mathematics Subject Classification ID

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

Related Items (23)

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Cites Work

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• Gaussian fluctuations of connectivities in the subcritical regime of percolation
• The Wulff construction and asymptotics of the finite cluster distribution for two-dimensional Bernoulli percolation
• Stability of the Wulff minimum and fluctuations in shape for large finite clusters in two-dimensional percolation
• Dobrushin-Kotecký-Shlosman theorem up to the critical temperature
• Approximation of subadditive functions and convergence rates in limiting-shape results
• Ornstein-Zernike theory for finite range Ising models above \(T_c\)
• Sharpness of the phase transition in percolation models
• Power-law corrections to exponential decay of connectivities and correlations in lattice models.
• Lower bounds on the connectivity function in all directions for Bernoulli percolation in two and three dimensions

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