Electronic Journal of Probability

Near-critical percolation in two dimensions

Pierre Nolin

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We give a self-contained and detailed presentation of Kesten's results that allow to relate critical and near-critical percolation on the triangular lattice. They constitute an important step in the derivation of the exponents describing the near-critical behavior of this model. For future use and reference, we also show how these results can be obtained in more general situations, and we state some new consequences.

Article information

Electron. J. Probab. Volume 13 (2008), paper no. 55, 1562-1623.

Accepted: 17 September 2008
First available in Project Euclid: 1 June 2016

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B43: Percolation [See also 60K35] 82B27: Critical phenomena

near-critical percolation arm events critical exponents

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Nolin, Pierre. Near-critical percolation in two dimensions. Electron. J. Probab. 13 (2008), paper no. 55, 1562--1623. doi:10.1214/EJP.v13-565. http://projecteuclid.org/euclid.ejp/1464819128.

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