@inproceedings{cbd836e7ad6e401faa966ab0d08300ec,
title = "Phase Transition for Tree-Rooted Maps",
abstract = "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.",
keywords = "Asymptotic Enumeration, Phase transition, Planar maps, Random trees",
author = "Marie Albenque and {\'E}ric Fusy and Z{\'e}phyr Salvy",
note = "Publisher Copyright: {\textcopyright} Marie Albenque, {\'E}ric Fusy, and Z{\'e}phyr Salvy.; 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, A of A 2024 ; Conference date: 17-06-2024 Through 21-06-2024",
year = "2024",
month = jul,
day = "1",
doi = "10.4230/LIPIcs.AofA.2024.6",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Cecile Mailler and Sebastian Wild",
booktitle = "35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, A of A 2024",
}