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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.08873 |
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| _version_ | 1866911420049784832 |
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| author | Gladkov, Nikita Zimin, Aleksandr |
| author_facet | Gladkov, Nikita Zimin, Aleksandr |
| contents | We show that a site percolation is a stronger model than a bond percolation. We use the van den Berg -- Kesten (vdBK) inequality to prove that site percolation on a neighborhood of a vertex of degree $4$ cannot be simulated even approximately by bond percolation, and develop a decision tree technique to prove the same for a neighborhood of a vertex of degree $3$. This technique can be used to obtain inequalities for connectedness probabilities, including a conjectured inequality of Erik Aas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08873 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bond percolation does not simulate site percolation Gladkov, Nikita Zimin, Aleksandr Probability 60K35 (Primary) 05C80 (Secondary) We show that a site percolation is a stronger model than a bond percolation. We use the van den Berg -- Kesten (vdBK) inequality to prove that site percolation on a neighborhood of a vertex of degree $4$ cannot be simulated even approximately by bond percolation, and develop a decision tree technique to prove the same for a neighborhood of a vertex of degree $3$. This technique can be used to obtain inequalities for connectedness probabilities, including a conjectured inequality of Erik Aas. |
| title | Bond percolation does not simulate site percolation |
| topic | Probability 60K35 (Primary) 05C80 (Secondary) |
| url | https://arxiv.org/abs/2404.08873 |