Uniform attachment with freezing: Scaling limits
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917632118095872 |
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| author | Bellin, Étienne Blanc-Renaudie, Arthur Kammerer, Emmanuel Kortchemski, Igor |
| author_facet | Bellin, Étienne Blanc-Renaudie, Arthur Kammerer, Emmanuel Kortchemski, Igor |
| contents | We investigate scaling limits of trees built by uniform attachment with freezing, which is a variant of the classical model of random recursive trees introduced in a companion paper. Here vertices are allowed to freeze, and arriving vertices cannot be attached to already frozen ones. We identify a phase transition when the number of non-frozen vertices roughly evolves as the total number of vertices to a given power. In particular, we observe a critical regime where the scaling limit is a random compact real tree, closely related to a time non-homogenous Kingman coalescent process identified by Aldous. Interestingly, in this critical regime, a condensation phenomenon can occur. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_00484 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniform attachment with freezing: Scaling limits Bellin, Étienne Blanc-Renaudie, Arthur Kammerer, Emmanuel Kortchemski, Igor Probability 60D05 60F05 We investigate scaling limits of trees built by uniform attachment with freezing, which is a variant of the classical model of random recursive trees introduced in a companion paper. Here vertices are allowed to freeze, and arriving vertices cannot be attached to already frozen ones. We identify a phase transition when the number of non-frozen vertices roughly evolves as the total number of vertices to a given power. In particular, we observe a critical regime where the scaling limit is a random compact real tree, closely related to a time non-homogenous Kingman coalescent process identified by Aldous. Interestingly, in this critical regime, a condensation phenomenon can occur. |
| title | Uniform attachment with freezing: Scaling limits |
| topic | Probability 60D05 60F05 |
| url | https://arxiv.org/abs/2308.00484 |