A Harris-Kesten theorem for confetti percolation

Details A Harris-Kesten theorem for confetti percolation A Harris-Kesten theorem for confetti percolation

2012-04-26

arxiv.org/abs/1204.5837v1

Mathematics

Probability

27 pages, 15 figures

Scientific paper

Percolation properties of the dead leaves model, also known as confetti percolation, are considered. More precisely, we prove that the critical probability for confetti percolation with square-shaped grains is 1/2. This result is related to a question of Benjamini and Schramm concerning disk-shaped grains and can be seen as a variant of the Harris-Kesten theorem for bond percolation. The proof is based on techniques developed by Bollob\'as and Riordan to determine the critical probability for Voronoi and Johnson-Mehl percolation.

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