Duminil-Copin H, Hartarsky I. Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules.
Probab Theory Relat Fields 2024;
190:445-483. [PMID:
39279827 PMCID:
PMC11393198 DOI:
10.1007/s00440-024-01310-3]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2023] [Revised: 06/05/2024] [Accepted: 07/27/2024] [Indexed: 09/18/2024]
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.
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