Subcritical monotone cellular automata

We study monotone cellular automata (also known as 𝒰‐bootstrap percolation) in ℤd$$ {\mathbb{Z}}^d $$ with random initial configurations. Confirming a conjecture of Balister, Bollobás, Przykucki and Smith, who proved the corresponding result in two dimensions, we show that the critical probability i...

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Bibliographic Details
Published in:Random structures & algorithms Vol. 64; no. 1; pp. 38 - 61
Main Authors: Balister, Paul, Bollobás, Béla, Morris, Robert, Smith, Paul
Format: Journal Article
Language:English
Published: New York John Wiley & Sons, Inc 01.01.2024
Wiley Subscription Services, Inc
Subjects:
bootstrap percolation
Cellular automata
Percolation
universality
ISSN:1042-9832, 1098-2418
Online Access:Get full text
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Summary:We study monotone cellular automata (also known as 𝒰‐bootstrap percolation) in ℤd$$ {\mathbb{Z}}^d $$ with random initial configurations. Confirming a conjecture of Balister, Bollobás, Przykucki and Smith, who proved the corresponding result in two dimensions, we show that the critical probability is non‐zero for all subcritical models.
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ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.21174