Open Access
2014 The shape of large balls in highly supercritical percolation
Anne-Laure Basdevant, Nathanaël Enriquez, Lucas Gerin, Jean-Baptiste Gouéré
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Electron. J. Probab. 19: 1-14 (2014). DOI: 10.1214/EJP.v19-3062


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.


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Anne-Laure Basdevant. Nathanaël Enriquez. Lucas Gerin. Jean-Baptiste Gouéré. "The shape of large balls in highly supercritical percolation." Electron. J. Probab. 19 1 - 14, 2014.


Accepted: 28 February 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1294.60118
MathSciNet: MR3174838
Digital Object Identifier: 10.1214/EJP.v19-3062

Primary: 60K35
Secondary: 82B43

Keywords: First-passage percolation , Supercritical percolation , TASEP

Vol.19 • 2014
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