Electronic Journal of Probability

The shape of large balls in highly supercritical percolation

Anne-Laure Basdevant, Nathanaël Enriquez, Lucas Gerin, and Jean-Baptiste Gouéré

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We exploit a connection between distances in the infinite percolation cluster, when the parameter is close to one, and the discrete-time TASEP on Z. This shows that when the parameter goes to one, large balls in the cluster are asymptotically shaped near the axes like arcs of parabola.

Article information

Electron. J. Probab., Volume 19 (2014), paper no. 26, 14 pp.

Accepted: 28 February 2014
First available in Project Euclid: 4 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]

first-passage percolation supercritical percolation TASEP

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Basdevant, Anne-Laure; Enriquez, Nathanaël; Gerin, Lucas; Gouéré, Jean-Baptiste. The shape of large balls in highly supercritical percolation. Electron. J. Probab. 19 (2014), paper no. 26, 14 pp. doi:10.1214/EJP.v19-3062. https://projecteuclid.org/euclid.ejp/1465065668

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