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arXiv:math/0412510 [math.PR]AbstractReferencesReviewsResources

Sharp thresholds and percolation in the plane

Bela Bollobas, Oliver Riordan

Published 2004-12-28, updated 2005-10-04Version 2

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.

Comments: 28 pages, 8 figures. Minor revisions and additions. To appear in Random Structures and Algorithms
Journal: Random Structures and Algorithms 29 (2006), 524--548.
Categories: math.PR, math.CO
Subjects: 60K35, 82B43
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