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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Vydáno v:Random structures & algorithms Ročník 64; číslo 1; s. 38 - 61
Hlavní autoři: Balister, Paul, Bollobás, Béla, Morris, Robert, Smith, Paul
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York John Wiley & Sons, Inc 01.01.2024
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Témata:
bootstrap percolation
Cellular automata
Percolation
universality
ISSN:1042-9832, 1098-2418
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.21174