JournalsjemsVol. 28, No. 11pp. 4725–4796

Universality for monotone cellular automata

  • Paul Balister

    University of Oxford, UK

  • Béla Bollobás

    University of Cambridge, UK; University of Memphis, USA

  • Robert Morris

    IMPA, Rio de Janeiro, Brazil

  • Paul Smith

    London, UK
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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. 28 (2026), no. 11, pp. 4725–4796

DOI 10.4171/JEMS/1666