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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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Table of 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.