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November 2017 The sharp threshold for the Duarte model
Béla Bollobás, Hugo Duminil-Copin, Robert Morris, Paul Smith
Ann. Probab. 45(6B): 4222-4272 (November 2017). DOI: 10.1214/16-AOP1163


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.


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Béla Bollobás. Hugo Duminil-Copin. Robert Morris. Paul Smith. "The sharp threshold for the Duarte model." Ann. Probab. 45 (6B) 4222 - 4272, November 2017.


Received: 1 March 2016; Revised: 1 October 2016; Published: November 2017
First available in Project Euclid: 12 December 2017

zbMATH: 06838119
MathSciNet: MR3737910
Digital Object Identifier: 10.1214/16-AOP1163

Primary: 60K35
Secondary: 60C05

Keywords: Bootstrap percolation , critical probability , Duarte model , monotone cellular automata , sharp threshold

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.45 • No. 6B • November 2017
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