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arXiv · 1305.0104

The shape of large balls in highly supercritical percolation

Anne-Laure Basdevant·Nathanaël Enriquez·Lucas Gerin·Jean-Baptiste Gouéré
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Abstract

We exploit a connection between distances in the infinite percolation cluster, when the parameter is close to one, and the discrete-time TASEP on $\mathbb{Z}$. 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. 2013-05-01. The shape of large balls in highly supercritical percolation. https://arxiv.org/abs/1305.0104

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