Sharp thresholds and percolation in the plane
Probability
2007-05-23 v2 Combinatorics
Abstract
Recently, the authors showed that the critical probability for random Voronoi percolation in the plane is 1/2. A by-product of the method was a short proof of the Harris-Kesten Theorem concerning bond percolation in the planar square lattice. The aim of this paper is to show that the same techniques can be applied to many other planar percolation models, both to obtain short proofs of known results, and to prove new ones.
Cite
@article{arxiv.math/0412510,
title = {Sharp thresholds and percolation in the plane},
author = {Bela Bollobas and Oliver Riordan},
journal= {arXiv preprint arXiv:math/0412510},
year = {2007}
}
Comments
28 pages, 8 figures. Minor revisions and additions. To appear in Random Structures and Algorithms