Electronic Journal of Probability

On the Asymptotic Internal Path Length and the Asymptotic Wiener Index of Random Split Trees

Goetz Olaf Munsonius

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The random split tree introduced by Devroye (1999) is considered. We derive a second order expansion for the mean of its internal path length and furthermore obtain a limit law by the contraction method. As an assumption we need the splitter having a Lebesgue density and mass in every neighborhood of 1. We use properly stopped homogeneous Markov chains, for which limit results in total variation distance as well as renewal theory are used. Furthermore, we extend this method to obtain the corresponding results for the Wiener index.

Article information

Electron. J. Probab., Volume 16 (2011), paper no. 35, 1020-1047.

Accepted: 1 June 2011
First available in Project Euclid: 1 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems
Secondary: 68P05: Data structures 05C05: Trees

random trees probabilistic analysis of algorithms internal path length Wiener index

This work is licensed under aCreative Commons Attribution 3.0 License.


Munsonius, Goetz Olaf. On the Asymptotic Internal Path Length and the Asymptotic Wiener Index of Random Split Trees. Electron. J. Probab. 16 (2011), paper no. 35, 1020--1047. doi:10.1214/EJP.v16-889. https://projecteuclid.org/euclid.ejp/1464820204

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