Universality for monotone cellular automata
Probability
2022-11-08 v3 Mathematical Physics
Combinatorics
math.MP
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 Bollob\'as, Duminil-Copin, Morris and Smith.
Cite
@article{arxiv.2203.13806,
title = {Universality for monotone cellular automata},
author = {Paul Balister and Béla Bollobás and Robert Morris and Paul Smith},
journal= {arXiv preprint arXiv:2203.13806},
year = {2022}
}
Comments
65 pages, 2 figures, minor update, expanded outline of the proof