The shape of large balls in highly supercritical percolation

Anne-Laure Basdevant (Université Paris Ouest Nanterre)
Nathanaël Enriquez (Université Paris Ouest Nanterre)
Lucas Gerin (École Polytechnique)
Jean-Baptiste Gouéré (Université d'Orléans)


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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Pages: 1-14

Publication Date: February 28, 2014

DOI: 10.1214/EJP.v19-3062


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