On a sufficient condition for explosion in CMJ branching processes and applications to recursive trees

Tejas Iyer

doi:10.1214/24-ecp616

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arXiv · 2312.14147

On a sufficient condition for explosion in CMJ branching processes and applications to recursive trees

Tejas Iyer

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Abstract

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-Barab\'asi model, or preferential attachment tree with multiplicative fitness.

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Tejas Iyer. 2023-12-21. On a sufficient condition for explosion in CMJ branching processes and applications to recursive trees. https://doi.org/10.1214/24-ecp616

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