The Annals of Probability

Distances in the highly supercritical percolation cluster

Anne-Laure Basdevant, Nathanaël Enriquez, and Lucas Gerin

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Abstract

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

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

Dates
First available in Project Euclid: 20 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.aop/1384957790

Digital Object Identifier
doi:10.1214/12-AOP802

Mathematical Reviews number (MathSciNet)
MR3161477

Zentralblatt MATH identifier
1290.60099

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

Keywords
First-passage percolation supercritical percolation TASEP

Citation

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. https://projecteuclid.org/euclid.aop/1384957790


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