Abstract
The decreasing Markov chain on {1,2,3, …} with transition probabilities arises as a key component of the analysis of the beta-splitting random tree model. We give a direct and almost self-contained “probability” treatment of its occupation probabilities, as a counterpart to a more sophisticated but perhaps opaque derivation using a limit continuum tree structure and Mellin transforms.
Acknowledgments
This article is part of a broad project with Boris Pittel. We thank Alexander Iksanov, Luca Pratelli and Pietro Rigo for discussion of alternate proofs, and we thank reviewers for careful reading and kind comments.
Citation
David J. Aldous. Svante Janson. Xiaodan Li. "The harmonic descent chain." Electron. Commun. Probab. 29 1 - 10, 2024. https://doi.org/10.1214/24-ECP645
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