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November 2013 Distances in the highly supercritical percolation cluster
Anne-Laure Basdevant, Nathanaël Enriquez, Lucas Gerin
Ann. Probab. 41(6): 4342-4358 (November 2013). DOI: 10.1214/12-AOP802


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).


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Anne-Laure Basdevant. Nathanaël Enriquez. Lucas Gerin. "Distances in the highly supercritical percolation cluster." Ann. Probab. 41 (6) 4342 - 4358, November 2013.


Published: November 2013
First available in Project Euclid: 20 November 2013

zbMATH: 1290.60099
MathSciNet: MR3161477
Digital Object Identifier: 10.1214/12-AOP802

Primary: 60K35 , 82B43

Keywords: First-passage percolation , Supercritical percolation , TASEP

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 6 • November 2013
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