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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2208.08346 |
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| _version_ | 1866929317754175488 |
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| author | Gracar, Peter Grauer, Arne |
| author_facet | Gracar, Peter Grauer, Arne |
| contents | We study the contact process on a class of geometric random graphs with scale-free degree distribution, defined on a Poisson point process on $\mathbb{R}^d$. This class includes the age-dependent random connection model and the soft Boolean model. In the ultrasmall regime of these random graphs we provide exact asymptotics for the non-extinction probability when the rate of infection spread is small and show for a finite version of these graphs that the extinction time is of exponential order in the size of the graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_08346 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The contact process on scale-free geometric random graphs Gracar, Peter Grauer, Arne Probability 05C80 (Primary), 82C22 (Secondary) We study the contact process on a class of geometric random graphs with scale-free degree distribution, defined on a Poisson point process on $\mathbb{R}^d$. This class includes the age-dependent random connection model and the soft Boolean model. In the ultrasmall regime of these random graphs we provide exact asymptotics for the non-extinction probability when the rate of infection spread is small and show for a finite version of these graphs that the extinction time is of exponential order in the size of the graph. |
| title | The contact process on scale-free geometric random graphs |
| topic | Probability 05C80 (Primary), 82C22 (Secondary) |
| url | https://arxiv.org/abs/2208.08346 |