Sharp thresholds and percolation in the plane

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.

28 pages, 8 figures. Minor revisions and additions. To appear in Random Structures and Algorithms

References in corpus (3)

• The critical probability for random Voronoi percolation in the plane is 1/2
• A short proof of the Harris-Kesten Theorem
• A note on the Harris-Kesten Theorem

Cited by in corpus (4)

• Percolation on self-dual polygon configurations
• Sharpness of the percolation transition in the two-dimensional contact process
• Approximate zero-one laws and sharpness of the percolation transition in a class of models including two-dimensional Ising percolation
• A Harris-Kesten theorem for confetti percolation