The sharp threshold for the Duarte model

Wednesday, 16 March, 2016

Published in: 

arXiv:1603.05237

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.

Author(s): 

Béla Bollobás
Hugo Duminil-Copin
Robert Morris
Paul Smith