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The shape of large balls in highly supercritical percolation

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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https://hal.archives-ouvertes.fr/hal-00819221
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Submitted on : Tuesday, April 30, 2013 - 2:54:33 PM
Last modification on : Friday, March 27, 2020 - 3:31:16 AM
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  • HAL Id : hal-00819221, version 1
  • ARXIV : 1305.0104

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Anne-Laure Basdevant, Nathanaël Enriquez, Lucas Gerin, Jean-Baptiste Gouéré. The shape of large balls in highly supercritical percolation. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2014, pp.DOI: 10.1214/EJP.v19-3062. ⟨hal-00819221⟩

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