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.
https://hal.archives-ouvertes.fr/hal-00819221
Contributeur : Jean-Baptiste Gouéré <>
Soumis le : mardi 30 avril 2013 - 14:54:33
Dernière modification le : jeudi 27 avril 2017 - 09:46:36
Document(s) archivé(s) le : mardi 4 avril 2017 - 02:02:20
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>
