Scaling Limits of Discrete Aggregation Trees

Haastert, Jeroen, van (2025) Scaling Limits of Discrete Aggregation Trees. Master's Thesis / Essay, Mathematics.

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Abstract

In this thesis, we study the scaling limit of uniform random labeled rooted trees T_n to the continuum random tree (CRT), realized via the stick-breaking construction, in the Gromov--Hausdorff--Prokhorov topology. The discrete tree T_n is sampled using the Foata--Fuchs bijection, which can be regarded as the discrete analogue of the stick-breaking construction. We generalize existing results by introducing two families of non-uniform random labeled trees T_{n,beta} and T_{n, gamma} whose scaling limits are variants of the CRT constructed from Poisson point processes with intensities t^beta dt and ln^gamma(t+1)dt respectively. In the latter case, we find a compactness threshold at gamma = 1: for gamma > 1, the limiting tree T_gamma is compact almost surely, whereas for gamma \le 1 the tree T_gamma is almost surely non-compact.

Item Type:	Thesis (Master's Thesis / Essay)
Supervisor name:	Donderwinkel, S.A. and Bonnet, G.F.Y.
Degree programme:	Mathematics
Thesis type:	Master's Thesis / Essay
Language:	English
Date Deposited:	10 Dec 2025 10:16
Last Modified:	10 Dec 2025 10:16
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/37167

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