학술논문

Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules
Document Type
Working Paper
Source
Subject
Mathematics - Probability
60K35, 60C05
Language
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.
Comment: 36 pages, 5 figures, thoroughly revised presentation