The harmonic descent chain
David Aldous, Svante Janson, Xiaodan Li · Electronic Communications in Probability · 2024
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.