Anisotropic non-oriented bond percolation in high dimensions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916546128904192 |
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| author | Gomes, Pablo A. Pereira, Alan Sanchis, Remy |
| author_facet | Gomes, Pablo A. Pereira, Alan Sanchis, Remy |
| contents | We consider inhomogeneous non-oriented Bernoulli bond percolation on $\mathbb{Z}^d$, where each edge has a parameter depending on its direction. We prove that, under certain conditions, if the sum of the parameters is strictly greater than 1/2, we have percolation in sufficiently high dimensions. The main tool is a dynamical coupling between models for different dimensions with different sets of parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_09083 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Anisotropic non-oriented bond percolation in high dimensions Gomes, Pablo A. Pereira, Alan Sanchis, Remy Probability Mathematical Physics 60K35, 82B43 We consider inhomogeneous non-oriented Bernoulli bond percolation on $\mathbb{Z}^d$, where each edge has a parameter depending on its direction. We prove that, under certain conditions, if the sum of the parameters is strictly greater than 1/2, we have percolation in sufficiently high dimensions. The main tool is a dynamical coupling between models for different dimensions with different sets of parameters. |
| title | Anisotropic non-oriented bond percolation in high dimensions |
| topic | Probability Mathematical Physics 60K35, 82B43 |
| url | https://arxiv.org/abs/2106.09083 |