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.
"The sharp threshold for the Duarte model." Ann. Probab. 45 (6B) 4222 - 4272, November 2017. https://doi.org/10.1214/16-AOP1163