The sharp threshold for the duarte model
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 ofMountford from 1995, and is the first result of its type for a model with drift.
Annals of Probability
Bollobás, B., Duminil-Copin, H., Morris, R., & Smith, P. (2017). The sharp threshold for the duarte model. Annals of Probability, 45 (6), 4222-4272. https://doi.org/10.1214/16-AOP1163