A star is born: Explosive Crump-Mode-Jagers branching processes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908774607880192 |
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| author | Lodewijks, Bas |
| author_facet | Lodewijks, Bas |
| contents | We study a family of Crump--Mode--Jagers branching processes in random environment that explode, i.e. that grow infinitely large in finite time with positive probability. Building on recent work of the author and Iyer (``On the structure of genealogical trees associated with explosive Crump--Mode--Jagers branching processes", arXiv:2311.14664, 2023), we weaken certain assumptions required to prove that the branching process, at the time of explosion, contains a (unique) individual with infinite offspring. We then apply these results to super-linear preferential attachment models. In particular, we fill gaps in some of the cases analysed in Appendix A of the work of the author and Iyer and study a large range of previously unattainable cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18749 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A star is born: Explosive Crump-Mode-Jagers branching processes Lodewijks, Bas Probability We study a family of Crump--Mode--Jagers branching processes in random environment that explode, i.e. that grow infinitely large in finite time with positive probability. Building on recent work of the author and Iyer (``On the structure of genealogical trees associated with explosive Crump--Mode--Jagers branching processes", arXiv:2311.14664, 2023), we weaken certain assumptions required to prove that the branching process, at the time of explosion, contains a (unique) individual with infinite offspring. We then apply these results to super-linear preferential attachment models. In particular, we fill gaps in some of the cases analysed in Appendix A of the work of the author and Iyer and study a large range of previously unattainable cases. |
| title | A star is born: Explosive Crump-Mode-Jagers branching processes |
| topic | Probability |
| url | https://arxiv.org/abs/2411.18749 |