English

Crossing probabilities for Voronoi percolation

Probability 2015-07-31 v2

Abstract

We prove that the standard Russo-Seymour-Welsh theory is valid for Voronoi percolation. This implies that at criticality the crossing probabilities for rectangles are bounded by constants depending only on their aspect ratio. This result has many consequences, such as the polynomial decay of the one-arm event at criticality.

Keywords

Cite

@article{arxiv.1410.6773,
  title  = {Crossing probabilities for Voronoi percolation},
  author = {Vincent Tassion},
  journal= {arXiv preprint arXiv:1410.6773},
  year   = {2015}
}

Comments

14 pages, 3 figures

R2 v1 2026-06-22T06:35:44.688Z