Percolation with random one-dimensional reinforcements
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | Nascimento, A. Sanchis, R. Ungaretti, D. |
| author_facet | Nascimento, A. Sanchis, R. Ungaretti, D. |
| contents | We study inhomogeneous Bernoulli bond percolation on the graph $G \times \mathbb{Z}$, where $G$ is a connected quasi-transitive graph. The inhomogeneity is introduced through a random region $R$ around the origin axis $\{0\}\times\mathbb{Z}$, where each edge in $R$ is open with probability $q$ and all other edges are open with probability $p$. When the region $R$ is defined by stacking or overlapping boxes with random radii centered along the origin axis, we derive conditions on the moments of the radii, based on the growth properties of $G$, so that for any subcritical $p$ and any $q<1$, the non-percolative phase persists. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08614 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Percolation with random one-dimensional reinforcements Nascimento, A. Sanchis, R. Ungaretti, D. Probability 60K35, 60K37 We study inhomogeneous Bernoulli bond percolation on the graph $G \times \mathbb{Z}$, where $G$ is a connected quasi-transitive graph. The inhomogeneity is introduced through a random region $R$ around the origin axis $\{0\}\times\mathbb{Z}$, where each edge in $R$ is open with probability $q$ and all other edges are open with probability $p$. When the region $R$ is defined by stacking or overlapping boxes with random radii centered along the origin axis, we derive conditions on the moments of the radii, based on the growth properties of $G$, so that for any subcritical $p$ and any $q<1$, the non-percolative phase persists. |
| title | Percolation with random one-dimensional reinforcements |
| topic | Probability 60K35, 60K37 |
| url | https://arxiv.org/abs/2406.08614 |