2016/03/16 by Béla Bollobás, Bollobás, Béla, Hugo Duminil-Copin +5
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #math.CO #math.PR
paper · pdf · doi:10.48550/arxiv.1603.05237
47 pages, 7 figures. To appear, Annals of Probability
arxiv created 2016/10/10 · arxiv updated 2016/10/11
The class of critical bootstrap percolation models in two dimensions was recently introduced by Bollobás, Smith and Uzzell, and the critical threshold for percolation was determined up to a constant factor for all such models by the authors of this paper. Here we develop and refine the techniques introduced in that paper in order to determine a sharp threshold for the Duarte model. This resolves a question of Mountford from 1995, and is the first result of its type for a model with drift.