Perron--Frobenius theorem for a general tree-valued growth-fragmentation-isolation process

Chenlin Gu; Mingyuan Shen; Ronghang Zhang

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arXiv · 2606.24599

Perron--Frobenius theorem for a general tree-valued growth-fragmentation-isolation process

Chenlin Gu·Mingyuan Shen·Ronghang Zhang

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Abstract

A general tree-valued dynamics is considered in continuous time: new vertices are added, and the percolation happens on the links, and the connected components can be frozen. The model is an infinite-type branching process. The main result establishes the Perron--Frobenius type theorem on this model, which extends the previous work [Ann. Appl. Probab. 33 (6B) 5233 - 5278]. The proof does not rely on any property of the uniform random recursive tree.

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Chenlin Gu, Mingyuan Shen, Ronghang Zhang. 2026-06-23. Perron--Frobenius theorem for a general tree-valued growth-fragmentation-isolation process. https://arxiv.org/abs/2606.24599

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