On leaf related statistics in recursive tree models

S. Altok and Ü. Işlak

Statistics & Probability Letters, 2017, vol. 121, issue C, 61-69

Abstract: Using a bijection between a uniformly random permutation and a uniform recursive tree (URT), we give a simple proof of a recent result of Zhang that shows the asymptotic normality of the number of leaves in a URT with convergence rates. We also show that a similar result holds for a more general class of statistics related to URTs, that we call the number of runs of leaves in a URT. The second, and the main, purpose of the current note is to introduce and to study a non-uniform recursive tree model by exploiting the bijection between permutations and recursive trees. This may provide a useful framework for constructing various types of random trees.

Keywords: Uniform recursive tree; Number of leaves; Central limit theorem; Stein’s method; Riffle-shuffle distribution (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2016.10.007

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