English

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

R2 v1 2026-06-21T19:33:36.320Z