Scaling limit of trees with vertices of fixed degrees and heights
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910041830850560 |
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| author | Blanc-Renaudie, Arthur Kammerer, Emmanuel |
| author_facet | Blanc-Renaudie, Arthur Kammerer, Emmanuel |
| contents | We consider large uniform random trees where we fix for each vertex its degree and height. We prove, under natural conditions of convergence for the profile, that those trees properly renormalized converge. To this end, we study the paths from random vertices to the root using coalescent processes. As an application, we obtain scaling limits of Bienaymé-Galton-Watson trees in varying environment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12897 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scaling limit of trees with vertices of fixed degrees and heights Blanc-Renaudie, Arthur Kammerer, Emmanuel Probability 60D05 60F05 We consider large uniform random trees where we fix for each vertex its degree and height. We prove, under natural conditions of convergence for the profile, that those trees properly renormalized converge. To this end, we study the paths from random vertices to the root using coalescent processes. As an application, we obtain scaling limits of Bienaymé-Galton-Watson trees in varying environment. |
| title | Scaling limit of trees with vertices of fixed degrees and heights |
| topic | Probability 60D05 60F05 |
| url | https://arxiv.org/abs/2409.12897 |