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arXiv · 2601.05906

Convergence to the Brownian CRT for critical branching Markov processe

Emma Horton·Ellen Powell
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Abstract

We prove an invariance principle for a general class of continuous time critical branching processes with finite variance (non-local) branching mechanism. We show that the genealogical trees, viewed as random compact metric measure spaces, converge under rescaling to the Brownian continuum random tree in the Gromov-Hausdorff-weak topology, establishing a universal scaling limit for critical finite variance branching processes.

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Emma Horton, Ellen Powell. 2026-01-09. Convergence to the Brownian CRT for critical branching Markov processe. https://arxiv.org/abs/2601.05906

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