Work

Phase Transition for Tree-Rooted Maps

Year: 2024

Type: conference-paper

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 $\sqrt{n/\log(n)}$ and $\sqrt{n}$.

Source: HAL (Le Centre pour la Communication Scientifique Directe)

DOI: 10.4230/lipics.aofa.2024.6

Authors: Albenque, Marie, Fusy, Éric, Salvy, Zéphyr

Institutions: Université Paris Cité, Institut de Recherche en Informatique Fondamentale, Centre National de la Recherche Scientifique, Laboratoire d'Informatique Gaspard-Monge, Université Gustave Eiffel

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Awards: A combinatorial study of Ising model on maps, Combinatorics of maps, meanders and multicurves, and its interactions