Phase transition for tree-rooted maps
| Autor: | Albenque, Marie, Fusy, Éric, Salvy, Zéphyr |
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| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 6:1-6:14 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4230/LIPIcs.AofA.2024.6 |
| Popis: | 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 $\sqrt{n}$. Comment: 14 pages |
| Databáze: | arXiv |
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