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Subcritical bootstrap percolation via Toom contours

Hartarsky, Ivailo; Szabo, Reka (2022), Subcritical bootstrap percolation via Toom contours, Electronic Communications in Probability, 27, p. 1-13. 10.1214/22-ECP496

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Type
Article accepté pour publication ou publié
Date
2022
Journal name
Electronic Communications in Probability
Volume
27
Publisher
Institute of Mathematical Statistics
Pages
1-13
Publication identifier
Metadata
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Author(s)
Hartarsky, Ivailo cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Szabo, Reka
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
In this note we provide an alternative proof of the fact that subcritical bootstrap percolation models have a positive critical probability in any dimension. The proof relies on a recent extension of the classical framework of Toom. This approach is not only simpler than the original multi-scale renormalisation proof of the result in two and more dimensions, but also gives significantly better bounds. As a byproduct, we improve the best known bounds for the stability threshold of Toom’s North-East-Center majority rule cellular automaton.
Subjects / Keywords
bootstrap percolation; Toom rule; North-East-Center majority; critical probability; stability threshold; Toom contour