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Subcritical monotone cellular automata

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By Robert Morris, Paul Smith, Paul Balister, Clerkenwell London
| pericles.pericles-prod.literatumonline.com
Abstract We study monotone cellular automata (also known as š’° -bootstrap percolation) in ā„¤ d $$ {\mathbb{Z}}^d $$ with random initial configurations. Confirming a conjecture of Balister, BollobĆ”s, Przykucki and Smith, who proved the corresponding result in two dimensions, we show that the critical probability is non-zero for all subcritical models. Open Research Not applicable (there is no data to share). REFERENCES 1, , , and , The critical length for growing a droplet, Mem. Amer. Math. Soc.
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