The extinction of the contact process in a one-dimensional random environment with long-range interactions
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914391900815360 |
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| author | Gomes, Pablo A. Hilário, Marcelo R. de Lima, Bernardo N. B. Mountford, Thomas |
| author_facet | Gomes, Pablo A. Hilário, Marcelo R. de Lima, Bernardo N. B. Mountford, Thomas |
| contents | We study the contact process on the long-range percolation cluster on $\mathbb{Z}$ where each edge $\langle i,j \rangle$ is open with probability $|i-j|^{-s}$ for $s> 2$. Using a renormalization procedure we apply Peierls-type argument to prove that the contact process dies out if the transmission rate is smaller than a critical threshold. Our methods involve the control of crossing probabilities for percolation on randomly-stretched lattices as in https://doi.org/10.1214/22-AAP1887. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17444 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The extinction of the contact process in a one-dimensional random environment with long-range interactions Gomes, Pablo A. Hilário, Marcelo R. de Lima, Bernardo N. B. Mountford, Thomas Probability 60K35, 82B43 We study the contact process on the long-range percolation cluster on $\mathbb{Z}$ where each edge $\langle i,j \rangle$ is open with probability $|i-j|^{-s}$ for $s> 2$. Using a renormalization procedure we apply Peierls-type argument to prove that the contact process dies out if the transmission rate is smaller than a critical threshold. Our methods involve the control of crossing probabilities for percolation on randomly-stretched lattices as in https://doi.org/10.1214/22-AAP1887. |
| title | The extinction of the contact process in a one-dimensional random environment with long-range interactions |
| topic | Probability 60K35, 82B43 |
| url | https://arxiv.org/abs/2506.17444 |