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

Hugo Duminil-Copin, Ivailo Hartarsky

24/3/23 Published in : arXiv:2303.13920

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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  • Statistical Mechanics

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  • Statistical Mechanics and Random Structures
  • Spectral gap problems in non-perturbative quantum theory

Regularity of conjugacies of linearizable generalized interval exchange transformations

A cavity quantum electrodynamics implementation of the Sachdev--Ye--Kitaev model

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