Convergence to the Brownian CRT for critical branching Markov processe
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866917192477442048 |
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| author | Horton, Emma Powell, Ellen |
| author_facet | Horton, Emma Powell, Ellen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05906 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergence to the Brownian CRT for critical branching Markov processe Horton, Emma Powell, Ellen Probability 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. |
| title | Convergence to the Brownian CRT for critical branching Markov processe |
| topic | Probability |
| url | https://arxiv.org/abs/2601.05906 |