The Annals of Probability

The sharp threshold for the Duarte model

Abstract

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.

Article information

Source
Ann. Probab., Volume 45, Number 6B (2017), 4222-4272.

Dates
Received: March 2016
Revised: October 2016
First available in Project Euclid: 12 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aop/1513069259

Digital Object Identifier
doi:10.1214/16-AOP1163

Mathematical Reviews number (MathSciNet)
MR3737910

Zentralblatt MATH identifier
06838119

Citation

Bollobás, Béla; Duminil-Copin, Hugo; Morris, Robert; Smith, Paul. The sharp threshold for the Duarte model. Ann. Probab. 45 (2017), no. 6B, 4222--4272. doi:10.1214/16-AOP1163. https://projecteuclid.org/euclid.aop/1513069259

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