On extinction and survival of the Bak-Sneppen model on arbitrary graphs
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912438282092544 |
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| author | Popov, Serguei Volkov, Stanislav |
| author_facet | Popov, Serguei Volkov, Stanislav |
| contents | We study the discrete Bak-Sneppen model introduced by Barbay and Kenyon (2001) "On the discrete Bak-Sneppen model of self-organized criticality". We extend their results as well as the non-triviality result of Meester and Znamenskiy (2002) for a finite segment of $\mathbb{Z}^1$ with the periodic boundary condition to a large class of graphs, by using coupling between the Bak-Sneppen model and the oriented percolation in a quadrant. This allows us to avoid dealing with the so-called avalanches, thus simplifying many arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15500 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On extinction and survival of the Bak-Sneppen model on arbitrary graphs Popov, Serguei Volkov, Stanislav Probability Mathematical Physics 60J20, 60K35, 82C22 We study the discrete Bak-Sneppen model introduced by Barbay and Kenyon (2001) "On the discrete Bak-Sneppen model of self-organized criticality". We extend their results as well as the non-triviality result of Meester and Znamenskiy (2002) for a finite segment of $\mathbb{Z}^1$ with the periodic boundary condition to a large class of graphs, by using coupling between the Bak-Sneppen model and the oriented percolation in a quadrant. This allows us to avoid dealing with the so-called avalanches, thus simplifying many arguments. |
| title | On extinction and survival of the Bak-Sneppen model on arbitrary graphs |
| topic | Probability Mathematical Physics 60J20, 60K35, 82C22 |
| url | https://arxiv.org/abs/2506.15500 |