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

Part of: Special processes

Published online by Cambridge University Press:  13 May 2020

ALEX D. RAMOS Open the ORCID record for ALEX D. RAMOS [Opens in a new window] ,
CALITÉIA S. SOUSA Open the ORCID record for CALITÉIA S. SOUSA [Opens in a new window] ,
PABLO M. RODRIGUEZ Open the ORCID record for PABLO M. RODRIGUEZ [Opens in a new window]  and
PAULA CADAVID Open the ORCID record for PAULA CADAVID [Opens in a new window]
ALEX D. RAMOS
Affiliation:
Department of Statistics, Universidade Federal de Pernambuco, Recife, PE, 50740-540, Brazil email [email protected]
CALITÉIA S. SOUSA
Affiliation:
Department of Statistics, Universidade Federal de Pernambuco, Recife, PE, 50740-540, Brazil email [email protected]
PABLO M. RODRIGUEZ*
Affiliation:
Department of Statistics, Universidade Federal de Pernambuco, Recife, PE, 50740-540, Brazil email [email protected]
PAULA CADAVID
Affiliation:
Universidade Federal do ABC, Santo André, SP, 09210-580, Brazil email [email protected]
*
✉[email protected]
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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.

Keywords

particle random processone-dimensional local interactionphase transitionStavskaya’s processprobabilistic cellular automata

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 3 , December 2020 , pp. 517 - 524
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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).

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