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

Hugo Duminil-Copin, Ivailo Hartarsky
Author Information
  1. Hugo Duminil-Copin: Université de Genève, Section de Mathématiques, 2-4 rue du Lièvre, 1211 Geneva, Switzerland.
  2. Ivailo Hartarsky: Research Unit of Probability, Faculty of Mathematics and Geoinformation, Institute of Statistics and Mathematical Methods in Economics, TU Wien, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria.

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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References

Commun Math Phys. 2024;405(1):13 [PMID: 38283710]

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