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

Published online by Cambridge University Press:  13 May 2020

ALEX D. RAMOS
Affiliation:
Department of Statistics, Universidade Federal de Pernambuco, Recife, PE, 50740-540, Brazil email alex@de.ufpe.br
CALITÉIA S. SOUSA
Affiliation:
Department of Statistics, Universidade Federal de Pernambuco, Recife, PE, 50740-540, Brazil email caliteia@de.ufpe.br
PABLO M. RODRIGUEZ
Affiliation:
Department of Statistics, Universidade Federal de Pernambuco, Recife, PE, 50740-540, Brazil email pablo@de.ufpe.br
PAULA CADAVID
Affiliation:
Universidade Federal do ABC, Santo André, SP, 09210-580, Brazil email pacadavid@gmail.com

Abstract

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.

Type
Research Article
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

This work has been partially supported by FAPESP (2017/10555-0), CNPq (Grant 304676/2016-0) and CAPES (under the Program MATH-AMSUD/CAPES 88881.197412/2018-01).

References

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