Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909401595510784 |
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| author | Duminil-Copin, Hugo Hartarsky, Ivailo |
| author_facet | Duminil-Copin, Hugo Hartarsky, Ivailo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_13920 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules Duminil-Copin, Hugo Hartarsky, Ivailo Probability 60K35, 60C05 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. |
| title | Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules |
| topic | Probability 60K35, 60C05 |
| url | https://arxiv.org/abs/2303.13920 |