On a sufficient condition for explosion in CMJ branching processes and applications to recursive trees
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916487482048512 |
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| author | Iyer, Tejas |
| author_facet | Iyer, Tejas |
| contents | We provide sufficient criteria for explosion in Crump-Mode-Jagers branching process, via the process producing an infinite path in finite time. As an application, we deduce a curious phase-transition in the infinite tree associated with a class of recursive tree models with fitness, showing that in one regime every node in the tree has infinite degree, whilst in another, the tree is locally finite, with a unique infinite path. The latter class encompasses many models studied in the literature, including the weighted random recursive tree, the preferential attachment tree with additive fitness, and the Bianconi-Barabási model, or preferential attachment tree with multiplicative fitness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14147 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On a sufficient condition for explosion in CMJ branching processes and applications to recursive trees Iyer, Tejas Probability 60J80, 90B15, 05C80 We provide sufficient criteria for explosion in Crump-Mode-Jagers branching process, via the process producing an infinite path in finite time. As an application, we deduce a curious phase-transition in the infinite tree associated with a class of recursive tree models with fitness, showing that in one regime every node in the tree has infinite degree, whilst in another, the tree is locally finite, with a unique infinite path. The latter class encompasses many models studied in the literature, including the weighted random recursive tree, the preferential attachment tree with additive fitness, and the Bianconi-Barabási model, or preferential attachment tree with multiplicative fitness. |
| title | On a sufficient condition for explosion in CMJ branching processes and applications to recursive trees |
| topic | Probability 60J80, 90B15, 05C80 |
| url | https://arxiv.org/abs/2312.14147 |