Subcritical monotone cellular automata

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 31 Jul 2023Embargo end date: 01 Mar 2022 United Kingdom English Publisher:WileyJournal:Random Structures & Algorithms, volume 64, pages 38-61 (issn: 1042-9832, eissn: 1098-2418,

Copyright policy )Funded by:EC | MALIG, NSF | Applications of Probabili...

Authors: Balister, P; Bollobás, B; Morris, R; Smith, P;

doi: 10.1002/rsa.21174 , 10.48550/arxiv.2203.01917

arXiv: 2203.01917

Subcritical monotone cellular automata

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Abstract

AbstractWe study monotone cellular automata (also known as ‐bootstrap percolation) in 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.

Country

United Kingdom

Related Organizations

University of Memphis
United States
University of Oxford
United Kingdom
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
France

Keywords

Cellular automata (computational aspects), Bootstrap, jackknife and other resampling methods, cellular automata, Probability (math.PR), Interacting random processes; statistical mechanics type models; percolation theory, Quantum computation, FOS: Mathematics, Mathematics - Combinatorics, universality, Combinatorics (math.CO), bootstrap percolation, Mathematics - Probability

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