The Annals of Probability

Distances in the highly supercritical percolation cluster

Anne-Laure Basdevant, Nathanaël Enriquez, and Lucas Gerin

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On the supercritical percolation cluster with parameter $p$, the distances between two distant points of the axis are asymptotically increased by a factor $1+\frac{1-p}{2}+o(1-p)$ with respect to the usual distance. The proof is based on an apparently new connection with the TASEP (totally asymmetric simple exclusion process).

Article information

Ann. Probab. Volume 41, Number 6 (2013), 4342-4358.

First available in Project Euclid: 20 November 2013

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Zentralblatt MATH identifier

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

First-passage percolation supercritical percolation TASEP


Basdevant, Anne-Laure; Enriquez, Nathanaël; Gerin, Lucas. Distances in the highly supercritical percolation cluster. Ann. Probab. 41 (2013), no. 6, 4342--4358. doi:10.1214/12-AOP802.

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