New methods to bound the critical probability in fractal percolation |
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Authors: | Henk Don |
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Institution: | Faculty of Science, Institute for Mathematics, Astrophysics, and Particle Physics, Radboud University Nijmegen, AJ Nijmegen, the Netherlands |
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Abstract: | We study the critical probability pc(M) in two‐dimensional M‐adic fractal percolation. To find lower bounds, we compare fractal percolation with site percolation. Fundamentally new is the construction of a computable increasing sequence that converges to pc(M). We prove that and . For the upper bounds, we introduce an iterative random process on a finite alphabet , which is easier to analyze than the original process. We show that and . © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 710–730, 2015 |
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Keywords: | fractal percolation critical probability upper and lower bounds |
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