The Harmonic Descent Chain

2024/05/08 by Aldous, David J., Janson, Svante, Li, Xiaodan · 2 citations
#60J10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2405.05102

Abstract

The decreasing Markov chain on \1,2,3, …\ with transition probabilities p(j,j-i) ∝ 1/i 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.

Cited by

• Some central limit theorems for critical beta-splitting tree
• Asymptotics for the harmonic descent chain and applications to critical beta-splitting trees

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