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

Hugo Duminil-Copin; Ivailo Hartarsky

doi:10.1007/s00440-024-01310-3

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arXiv · 2303.13920

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

Hugo Duminil-Copin·Ivailo Hartarsky

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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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Hugo Duminil-Copin, Ivailo Hartarsky. 2023-03-24. Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules. https://doi.org/10.1007/s00440-024-01310-3

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