New methods to bound the critical probability in fractal percolation. Issue 4 (31st July 2014) - Don, Henk
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 pc(2)>0.881 and pc(3)>0.784. For the upper bounds, we introduce an iterative random process on a finite alphabet A, which is easier to analyze than the original process. We show that pc(2)≤0.993, pc(3)≤0.940 and pc(4)≤0.972. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 710–730, 2015