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November 2015 On the number of leaves in a random recursive tree
Yazhe Zhang
Braz. J. Probab. Stat. 29(4): 897-908 (November 2015). DOI: 10.1214/14-BJPS252

Abstract

This paper studies the asymptotic behavior of the number of leaves $L_{n}$ in a random recursive tree $T_{n}$ with $n$ nodes. By utilizing the size-bias method, we derive an upper bound on the Wasserstein distance between the distribution of $L_{n}$ and a standard normal distribution. Furthermore, we obtain a weak version of an Erdös–Rényi type law and a large deviation principle for $L_{n}$.

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Yazhe Zhang. "On the number of leaves in a random recursive tree." Braz. J. Probab. Stat. 29 (4) 897 - 908, November 2015. https://doi.org/10.1214/14-BJPS252

Information

Received: 1 March 2014; Accepted: 1 June 2014; Published: November 2015
First available in Project Euclid: 17 September 2015

zbMATH: 1360.05081
MathSciNet: MR3397399
Digital Object Identifier: 10.1214/14-BJPS252

Rights: Copyright © 2015 Brazilian Statistical Association

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Vol.29 • No. 4 • November 2015
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