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Article Dans Une Revue Electronic Communications in Probability Année : 2022

Subcritical bootstrap percolation via Toom contours

Résumé

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.

Dates et versions

hal-03840504 , version 1 (05-11-2022)

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Ivailo Hartarsky, Réka Szabó. Subcritical bootstrap percolation via Toom contours. Electronic Communications in Probability, 2022, 27, ⟨10.1214/22-ECP496⟩. ⟨hal-03840504⟩
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