JournalsjemsOnline First

Universality for monotone cellular automata

  • Paul Balister

    University of Oxford, Oxford, UK
    ORCID

  • Béla Bollobás

    University of Cambridge, Cambridge, UK; University of Memphis, Memphis, USA
    ORCID

  • Robert Morris

    IMPA, Rio de Janeiro, Brazil
    ORCID

  • Paul Smith

    London, UK
Universality for monotone cellular automata cover
Download PDF

A subscription is required to access this article.

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