An improved lower bound for the critical parameter of the Stavskaya's\n process

2020/01/30 by A. D. Ramos, Caliteia S. Sousa, Ramos, Alex D. +5 · 1 citation
Computer Science · Mathematics · #60K35 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #advanced mathematical theories #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2001.11545

openalex publication_date 2020/01/30 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We consider the Stavskaya's process, which is a two-states Probabilistic\nCelular Automata defined on a one-dimensional lattice. The process is defined\nin such a way that the state of any vertex depends only on itself and on the\nstate of its right-adjacent neighbor. This process was one of the first\nmulticomponent systems with local interaction, for which has been proved\nrigorously the existence of a kind of phase transition. However, the exact\nlocalization of its critical value remains as an open problem. In this work we\nprovide a new lower bound for the critical value. The last one was obtained by\nAndrei Toom, fifty years ago.\n

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• An Improved Lower Bound for the Critical Parameter of the Stavskaya's Process via a Generalized Recurrent Method

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