The sharp threshold for the Duarte model

Bollobás, Béla; Duminil-Copin, Hugo; Morris, Robert; Smith, Paul
The class of critical bootstrap percolation models in two dimensions was recently introduced by Bollob$\backslash$'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.
Research areas:
Year:
2016
Type of Publication:
Article
Keywords:
bootstrap percolation; duarte model; monotone cellular automata; sharp threshold
Number:
317532
Pages:
1-47
Hits: 3083

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