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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.16357 |
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| _version_ | 1866917577456877568 |
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| author | Mester, Péter |
| author_facet | Mester, Péter |
| contents | We give an example of an invariant bond percolation process on the slab $\mathbb{Z}^2\times \{0,1\}$ with the property that it has infinitely many clusters whose critical percolation probability is strictly less than $1$. We also show that no such process can exist in $\mathbb{Z}^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16357 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invariant splitting of a slab into infinitely many robust clusters Mester, Péter Probability 60K35 We give an example of an invariant bond percolation process on the slab $\mathbb{Z}^2\times \{0,1\}$ with the property that it has infinitely many clusters whose critical percolation probability is strictly less than $1$. We also show that no such process can exist in $\mathbb{Z}^2$. |
| title | Invariant splitting of a slab into infinitely many robust clusters |
| topic | Probability 60K35 |
| url | https://arxiv.org/abs/2401.16357 |