Work

Convergence of trees with a given degree sequence and of their associated laminations

Year: 2025

Type: article

Abstract: In this paper, we study uniform rooted plane trees with given degree sequence. We show, under some natural hypotheses on the degree sequence, that these trees converge toward the so-called Inhomogeneous Continuum Random Tree after renormalisation. Our proof relies on the convergence of a modification of the well-known Lukasiewicz path. We also give a unified treatment of the limit, as the number of vertices tends to infinity, of the fragmentation process derived by cutting-down the edges of a tree with a given degree sequence, including its geometric representation by a lamination-valued process. The latter is a collection of nested laminations that are compact subsets of the unit disk made of non-crossing chords. In particular, we prove an equivalence between Gromov-weak convergence of discrete trees and the convergence of their associated lamination-valued processes.

Source: Stochastic Processes and their Applications

DOI: 10.1016/j.spa.2025.104816

Authors: Gabriel Berzunza Ojeda, Cecilia Holmgren, Paul Thévenin

Institutions: University of Liverpool, Uppsala University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,520

Funders: Ragnar Söderbergs stiftelse, Knut och Alice Wallenbergs Stiftelse, Vetenskapsrådet