Active Phase for Activated Random Walk on Z
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866911244367167488 |
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| author | Hoffman, Christopher Richey, Jacob Rolla, Leonardo T. |
| author_facet | Hoffman, Christopher Richey, Jacob Rolla, Leonardo T. |
| contents | We consider the Activated Random Walk model on $\mathbb{Z}$. In this model, each particle performs a continuous-time simple symmetric random walk, and falls asleep at rate $λ$. A sleeping particle does not move but it is reactivated in the presence of another particle. We show that for any sleep rate $λ< \infty$ if the density $ ζ$ is close enough to $1$ then the system stays active. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_09491 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Active Phase for Activated Random Walk on Z Hoffman, Christopher Richey, Jacob Rolla, Leonardo T. Probability Mathematical Physics We consider the Activated Random Walk model on $\mathbb{Z}$. In this model, each particle performs a continuous-time simple symmetric random walk, and falls asleep at rate $λ$. A sleeping particle does not move but it is reactivated in the presence of another particle. We show that for any sleep rate $λ< \infty$ if the density $ ζ$ is close enough to $1$ then the system stays active. |
| title | Active Phase for Activated Random Walk on Z |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2009.09491 |