ID: 2303.13920

Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules

March 24, 2023

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Hugo Duminil-Copin, Ivailo Hartarsky
Mathematics
Probability

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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