Using Mellin analysis of a limit exchangeable partition, the authors obtain full asymptotic expansions, the variance constant, the moment generating function, a CLT, and large deviation rates for the leaf height of the critical beta-splitting tree.
A comment on `The harmonic descent chain' by D.J. Aldous, S. Janson and X. Li
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abstract
An alternative proof is given for the main result of the article referred to in the title and published in ECP (2024). The proof exploits the theory of regenerative composition structures due to Gnedin and Pitman. The present article is a slight revision of my note written up in May 2024 as a reaction to the preprint arxiv.org version of the paper by Aldous, Janson and Li.
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The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height
Using Mellin analysis of a limit exchangeable partition, the authors obtain full asymptotic expansions, the variance constant, the moment generating function, a CLT, and large deviation rates for the leaf height of the critical beta-splitting tree.