Correction terms for the height of weighted recursive trees

2021/01/04 by Michel Pain, Pain, Michel, Delphin Sénizergues +1
Mathematics · Physics and Astronomy · #60G70 (Secondary) #60J80 (Primary) 05C05 #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:05C05 #msc:60G70 #msc:60J80

paper · pdf · doi:10.48550/arxiv.2101.01156

33 pages

openalex publication_date 2021/01/04 · arxiv created 2021/12/15 · arxiv updated 2021/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Under some assumptions on the sequence of weights, the first order for the height of such trees has been recently established in [Electron. J. Probab. 26 (2021), Paper No. 80] by one of the authors. In this paper, we obtain the second and third orders in the asymptotic expansion of the height of weighted recursive trees, under similar assumptions. Our methods are inspired from those used to prove similar results for branching random walks. Our results also apply to a related model of growing trees, called the preferential attachment tree with additive fitnesses.

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