The shape of large balls in highly supercritical percolation
Probability
2013-05-02 v1
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 . This shows that when the parameter goes to one, large balls in the cluster are asymptotically shaped near the axes like arcs of parabola.
Keywords
Cite
@article{arxiv.1305.0104,
title = {The shape of large balls in highly supercritical percolation},
author = {Anne-Laure Basdevant and Nathanaël Enriquez and Lucas Gerin and Jean-Baptiste Gouéré},
journal= {arXiv preprint arXiv:1305.0104},
year = {2013}
}