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The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height
David Aldous, Svante Janson
In the critical beta-splitting model of a random -leaf rooted tree, clades are recursively split into sub-clades, and a clade of leaves is split into sub-clades containing $…
The Critical Beta-splitting Random Tree III: The exchangeable partition representation and the fringe tree
David J. Aldous, Svante Janson
In the critical beta-splitting model of a random -leaf rooted tree, clades are recursively split into sub-clades, and a clade of leaves is split into sub-clades containing $…
The Harmonic Descent Chain
David J. Aldous, Svante Janson, Xiaodan Li
The decreasing Markov chain on \{1,2,3, \ldots\} with transition probabilities arises as a key component of the analysis of the beta-splitting random tree mo…
Markov chains and mappings of distributions on compact spaces
David J. Aldous, Shi Feng
Consider a compact metric space and a pair with and . For any probability distribution , define a Markov chain on by: from state…
Markov chains and mappings of distributions on compact spaces II: Numerics and Conjectures
David J. Aldous, Madelyn Cruz, Shi Feng
Consider a compact metric space and a pair with and . For any probability distribution , define a Markov chain on by: from state…
The distance problem on measured metric spaces
David J. Aldous, Guillaume Blanc, Nicolas Curien
What distributions arise as the distribution of the distance between two typical points in some measured metric space? This seems to be a surprisingly subtle problem. We conjecture…