Communication Dans Un Congrès Année : 2024

Phase Transition for Tree-Rooted Maps

Résumé

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.

Dates et versions

hal-04661772 , version 1 (25-07-2024)

Identifiants

Citer

Marie Albenque, Éric Fusy, Zéphyr Salvy. Phase Transition for Tree-Rooted Maps. 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024), Jun 2024, Bath, United Kingdom. pp.6:1-6:14, ⟨10.4230/LIPIcs.AofA.2024.6⟩. ⟨hal-04661772⟩
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