Universality for monotone cellular automata
Paul Balister
University of Oxford, Oxford, UKBéla Bollobás
University of Cambridge, Cambridge, UK; University of Memphis, Memphis, USARobert Morris
IMPA, Rio de Janeiro, BrazilPaul Smith
London, UK

Abstract
In this paper we study monotone cellular automata in 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 Bollobás, Duminil-Copin, Morris and Smith.
Cite this article
Paul Balister, Béla Bollobás, Robert Morris, Paul Smith, Universality for monotone cellular automata. J. Eur. Math. Soc. (2025), published online first
DOI 10.4171/JEMS/1666