Renewal Contact Processes: phase transition and survival
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866912862199349248 |
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| author | Fontes, Luiz Renato Mountford, Thomas S. Ungaretti, Daniel Vares, Maria Eulália |
| author_facet | Fontes, Luiz Renato Mountford, Thomas S. Ungaretti, Daniel Vares, Maria Eulália |
| contents | We refine previous results concerning the Renewal Contact Processes. We significantly widen the family of distributions for the interarrival times for which the critical value can be shown to be strictly positive. The result now holds for any dimension $d \ge 1$ and requires only a moment condition slightly stronger than finite first moment. For heavy-tailed interarrival times, we prove a Complete Convergence Theorem and examine when the contact process, conditioned on survival, can be asymptotically predicted knowing the renewal processes. We close with an example of distribution attracted to a stable law of index 1 for which the critical value vanishes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_06207 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Renewal Contact Processes: phase transition and survival Fontes, Luiz Renato Mountford, Thomas S. Ungaretti, Daniel Vares, Maria Eulália Probability 60K35, 60K05, 82B43 We refine previous results concerning the Renewal Contact Processes. We significantly widen the family of distributions for the interarrival times for which the critical value can be shown to be strictly positive. The result now holds for any dimension $d \ge 1$ and requires only a moment condition slightly stronger than finite first moment. For heavy-tailed interarrival times, we prove a Complete Convergence Theorem and examine when the contact process, conditioned on survival, can be asymptotically predicted knowing the renewal processes. We close with an example of distribution attracted to a stable law of index 1 for which the critical value vanishes. |
| title | Renewal Contact Processes: phase transition and survival |
| topic | Probability 60K35, 60K05, 82B43 |
| url | https://arxiv.org/abs/2101.06207 |