A Harris‐Kesten theorem for confetti percolation |
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Authors: | Christian Hirsch |
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Institution: | Faculty of Mathematics and Economics, Institute of Stochastics, Ulm University, Ulm, Germany |
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Abstract: | 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 leaves is 1/2. This result is related to a question of Benjamini and Schramm concerning disk‐shaped leaves and can be seen as a variant of the Harris‐Kesten theorem for bond percolation. The proof is based on techniques developed by Bollobás and Riordan to determine the critical probability for Voronoi and Johnson‐Mehl percolation. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 361–385, 2015 |
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Keywords: | dead leaves model confetti percolation RSW theorem sharp threshold dependent percolation |
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