Subcritical monotone cellular automata
Probability
2022-04-20 v2 Combinatorics
Abstract
We study monotone cellular automata (also known as -bootstrap percolation) in with random initial configurations. Confirming a conjecture of Balister, Bollob\'as, Przykucki and Smith, who proved the corresponding result in two dimensions, we show that the critical probability is non-zero for all subcritical models.
Keywords
Cite
@article{arxiv.2203.01917,
title = {Subcritical monotone cellular automata},
author = {Paul Balister and Béla Bollobás and Robert Morris and Paul Smith},
journal= {arXiv preprint arXiv:2203.01917},
year = {2022}
}
Comments
23 pages, 2 figures, added Theorem 7.1