English

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.

Keywords

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