AN IMPROVED LOWER BOUND FOR THE CRITICAL PARAMETER OF STAVSKAYA’S PROCESS

We consider Stavskaya’s process, which is a two-state probabilistic cellular automaton defined on a one-dimensional lattice. The state of any vertex depends only on itself and on the state of its right-adjacent neighbour. This process was one of the first multicomponent systems with local interactio...

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 2020-12, Vol.102 (3), p.517-524
Main Authors: RAMOS, ALEX D., SOUSA, CALITÉIA S., RODRIGUEZ, PABLO M., CADAVID, PAULA
Format: Article
Language:English
Subjects:
Cellular automata
Lower bounds
Phase transitions
Process parameters
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Summary:We consider Stavskaya’s process, which is a two-state probabilistic cellular automaton defined on a one-dimensional lattice. The state of any vertex depends only on itself and on the state of its right-adjacent neighbour. This process was one of the first multicomponent systems with local interaction for which the existence of a kind of phase transition has been rigorously proved. However, the exact localisation of its critical value remains as an open problem. We provide a new lower bound for the critical value.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972720000404