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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2407.16809 |
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| _version_ | 1866910539195613184 |
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| author | Albenque, Marie Fusy, Éric Salvy, Zéphyr |
| author_facet | Albenque, Marie Fusy, Éric Salvy, Zéphyr |
| contents | We introduce a model of tree-rooted planar maps weighted by their number of $2$-connected blocks. We study its enumerative properties and prove that it undergoes a phase transition. We give the distribution of the size of the largest $2$-connected blocks in the three regimes (subcritical, critical and supercritical) and further establish that the scaling limit is the Brownian Continuum Random Tree in the critical and supercritical regimes, with respective rescalings $\sqrt{n/\log(n)}$ and $\sqrt{n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16809 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Phase transition for tree-rooted maps Albenque, Marie Fusy, Éric Salvy, Zéphyr Probability Combinatorics We introduce a model of tree-rooted planar maps weighted by their number of $2$-connected blocks. We study its enumerative properties and prove that it undergoes a phase transition. We give the distribution of the size of the largest $2$-connected blocks in the three regimes (subcritical, critical and supercritical) and further establish that the scaling limit is the Brownian Continuum Random Tree in the critical and supercritical regimes, with respective rescalings $\sqrt{n/\log(n)}$ and $\sqrt{n}$. |
| title | Phase transition for tree-rooted maps |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2407.16809 |