Long-range contact process and percolation on a random lattice
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866916546135195648 |
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| author | Gomes, Pablo A. de Lima, Bernardo N. B. |
| author_facet | Gomes, Pablo A. de Lima, Bernardo N. B. |
| contents | We study the phase transition phenomena for long-range oriented percolation and contact process. We studied a contact process in which the range of each vertex are independent, updated dynamically and given by some distribution $N$. We also study an analogous oriented percolation model on the hyper-cubic lattice, here there is a special direction where long-range oriented bonds are allowed; the range of all vertices are given by an i.i.d. sequence of random variables with common distribution $N$. For both models, we prove some results about the existence of a phase transition in terms of the distribution $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_13531 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Long-range contact process and percolation on a random lattice Gomes, Pablo A. de Lima, Bernardo N. B. Probability 60K35, 82B43 We study the phase transition phenomena for long-range oriented percolation and contact process. We studied a contact process in which the range of each vertex are independent, updated dynamically and given by some distribution $N$. We also study an analogous oriented percolation model on the hyper-cubic lattice, here there is a special direction where long-range oriented bonds are allowed; the range of all vertices are given by an i.i.d. sequence of random variables with common distribution $N$. For both models, we prove some results about the existence of a phase transition in terms of the distribution $N$. |
| title | Long-range contact process and percolation on a random lattice |
| topic | Probability 60K35, 82B43 |
| url | https://arxiv.org/abs/2108.13531 |