The truncation property and continuity for the long-range contact process on $\mathbb{Z}^d$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| author | Bethuelsen, Stein Andreas Namugera, Frank |
| author_facet | Bethuelsen, Stein Andreas Namugera, Frank |
| contents | We consider a general class of contact processes on $\mathbb{Z}^d$ with potentially long-range interactions. By adapting well established renormalization arguments to the long-range setting we extend by now classical results for finite-range processes to this more general setting. Particularly, we provide general conditions on the decay of the interactions under which a supercritical process remains supercritical after truncation of the interaction parameter at a sufficiently large distance. Further, for the family of parameters satisfying this latter truncation property, we conclude that the probability of the process to never recover is continuous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15753 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The truncation property and continuity for the long-range contact process on $\mathbb{Z}^d$ Bethuelsen, Stein Andreas Namugera, Frank Probability 60K35, 82B43 We consider a general class of contact processes on $\mathbb{Z}^d$ with potentially long-range interactions. By adapting well established renormalization arguments to the long-range setting we extend by now classical results for finite-range processes to this more general setting. Particularly, we provide general conditions on the decay of the interactions under which a supercritical process remains supercritical after truncation of the interaction parameter at a sufficiently large distance. Further, for the family of parameters satisfying this latter truncation property, we conclude that the probability of the process to never recover is continuous. |
| title | The truncation property and continuity for the long-range contact process on $\mathbb{Z}^d$ |
| topic | Probability 60K35, 82B43 |
| url | https://arxiv.org/abs/2604.15753 |