Electronic Journal of Probability

Near-critical percolation in two dimensions

Pierre Nolin

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
http://projecteuclid.org/euclid.ejp/1464819128

Digital Object Identifier
doi:10.1214/EJP.v13-565

Mathematical Reviews number (MathSciNet)
MR2438816

Zentralblatt MATH identifier
1189.60182

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

Keywords
near-critical percolation arm events critical exponents

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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