Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules
arXiv:2303.13920 · doi:10.1007/s00440-024-01310-3
Abstract
We study two-dimensional critical bootstrap percolation models. We establish that a class of these models including all isotropic threshold rules with a convex symmetric neighbourhood, undergoes a sharp metastability transition. This extends previous instances proved for several specific rules. The paper supersedes a draft by Alexander Holroyd and the first author from 2012. While it served a role in the subsequent development of bootstrap percolation universality, we have chosen to adopt a more contemporary viewpoint in its present form.
37 pages, 6 figures, improved presentation, added section 6