Phase Transition for Tree-Rooted Maps

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publication35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, A of A 2024
EditorsCecile Mailler, Sebastian Wild
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959773294
DOIs
Publication statusPublished - 1 Jul 2024
Externally publishedYes
Event35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, A of A 2024 - Bath, United Kingdom
Duration: 17 Jun 202421 Jun 2024

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume302
ISSN (Print)1868-8969

Conference

Conference35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, A of A 2024
Country/TerritoryUnited Kingdom
CityBath
Period17/06/2421/06/24

Keywords

  • Asymptotic Enumeration
  • Phase transition
  • Planar maps
  • Random trees

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