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arXiv · 2203.13806

Universality for monotone cellular automata

Paul Balister·Béla Bollobás·Robert Morris·Paul Smith
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Abstract

In this paper we study monotone cellular automata in $d$ dimensions. We develop a general method for bounding the growth of the infected set when the initial configuration is chosen randomly, and then use this method to prove a lower bound on the critical probability for percolation that is sharp up to a constant factor in the exponent for every 'critical' model. This is one of three papers that together confirm the Universality Conjecture of Bollob\'as, Duminil-Copin, Morris and Smith.

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BibTeXRIS

Paul Balister, Béla Bollobás, Robert Morris, Paul Smith. 2022-03-25. Universality for monotone cellular automata. https://arxiv.org/abs/2203.13806

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