English

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 Z\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.

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}
}