The sharp threshold for the Duarte model
Probability
2016-10-11 v2 Combinatorics
Abstract
The class of critical bootstrap percolation models in two dimensions was recently introduced by Bollob\'as, 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.
Cite
@article{arxiv.1603.05237,
title = {The sharp threshold for the Duarte model},
author = {Béla Bollobás and Hugo Duminil-Copin and Robert Morris and Paul Smith},
journal= {arXiv preprint arXiv:1603.05237},
year = {2016}
}
Comments
47 pages, 7 figures. To appear, Annals of Probability