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

Alex D. Ramos; Caliteia S. Sousa; Pablo M. Rodriguez; Paula Cadavid

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arXiv · 2001.11545

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

Alex D. Ramos·Caliteia S. Sousa·Pablo M. Rodriguez·Paula Cadavid

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Abstract

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

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Alex D. Ramos, Caliteia S. Sousa, Pablo M. Rodriguez, Paula Cadavid. 2020-01-30. An improved lower bound for the critical parameter of the Stavskaya's process. https://arxiv.org/abs/2001.11545

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