Distances in the highly supercritical percolation cluster
Probability
2012-10-02 v2
Abstract
On the supercritical percolation cluster with parameter p, the distances between two distant points of the axis are asymptotically increased by a factor 1+(1-p)/2+o(1-p) with respect to the usual distance. The proof is based on an apparently new connection with the TASEP (totally asymmetric simple exclusion process).
Keywords
Cite
@article{arxiv.1111.2302,
title = {Distances in the highly supercritical percolation cluster},
author = {Anne-Laure Basdevant and Nathanaël Enriquez and Lucas Gerin},
journal= {arXiv preprint arXiv:1111.2302},
year = {2012}
}
Comments
15 pages