2022/04/12 by Michel Pain, Pain, Michel, Delphin Sénizergues +1
Mathematics · #60G70 #FOS: Mathematics #Geometry and complex manifolds #Markov Chains and Monte Carlo Methods #Primary 60J80 #Probability (math.PR) #Secondary 05C05 #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2204.05908
openalex publication_date 2022/04/12 · openalex created_date 2022/04/19 · openalex updated_date 2026/07/28
Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen at random with probability proportional to its weight. In the case where the total weight of the tree at step n grows polynomially in n, we obtained in (Pain-Sénizergues 2022) an asymptotic expansion for the height of the tree, which falls into the university class of the maximum of branching random walks. In this paper, we consider the case of a total weight growing sub-polynomially in n and obtain asymptotics for the height of the tree in several regimes, showing that universality is broken and exhibiting new behaviors.