A comment on `The harmonic descent chain' by D.J. Aldous, S. Janson and X. Li

TL;DR

This paper provides an alternative proof for a key result in a recent article on harmonic descent chains, utilizing regenerative composition structures, and offers a revised note in response to the original preprint.

Contribution

It introduces a new proof method based on regenerative composition structures for the main result of the referenced article.

Findings

Alternative proof of the main result

Utilizes regenerative composition structures theory

Revised note responding to preprint

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.