Largest component and sharpness in continuum percolation
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916023205101568 |
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| author | Küpper, Niclas Penrose, Mathew D. |
| author_facet | Küpper, Niclas Penrose, Mathew D. |
| contents | We investigate the behavior of large connected components in the Poisson Random Connection model in non-critical regimes with any bounded connection function. We show that the asymptotic size of the largest component restricted to a window grows logarithmically in the volume of that window in the subcritical case, and linearly in the supercritical case. We also prove a sharpness result saying that the order of the cluster at the origin has an exponentially decaying tail in the subcritical regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10715 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Largest component and sharpness in continuum percolation Küpper, Niclas Penrose, Mathew D. Probability 82B43 (Primary), 60D05 (Secondary) We investigate the behavior of large connected components in the Poisson Random Connection model in non-critical regimes with any bounded connection function. We show that the asymptotic size of the largest component restricted to a window grows logarithmically in the volume of that window in the subcritical case, and linearly in the supercritical case. We also prove a sharpness result saying that the order of the cluster at the origin has an exponentially decaying tail in the subcritical regime. |
| title | Largest component and sharpness in continuum percolation |
| topic | Probability 82B43 (Primary), 60D05 (Secondary) |
| url | https://arxiv.org/abs/2407.10715 |