2026-07-23T05:17:39Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:20441 2024-07-18T12:12:42Z ddc:004 open_access

Phase Transition for Tree-Rooted Maps Albenque, Marie Fusy, Éric Salvy, Zéphyr Asymptotic Enumeration Planar maps Random trees Phase transition 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 √{n/log(n)} and √n. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Marie Albenque and Éric Fusy and Zéphyr Salvy 2024 Is Part Of LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.AofA.2024.6 urn:nbn:de:0030-drops-204413 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.6 eng https://creativecommons.org/licenses/by/4.0/legalcode