Using Mellin analysis of a limit exchangeable partition, the authors obtain full asymptotic expansions, the variance constant, the moment generating function, a CLT, and large deviation rates for the leaf height of the critical beta-splitting tree.
Random Fragmentation and Coagulation Processes , volume 102 of Cambridge Studies in Advanced Mathematics
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The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height
Using Mellin analysis of a limit exchangeable partition, the authors obtain full asymptotic expansions, the variance constant, the moment generating function, a CLT, and large deviation rates for the leaf height of the critical beta-splitting tree.