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