Electronic Journal of Probability
- Electron. J. Probab.
- Volume 16 (2011), paper no. 35, 1020-1047.
On the Asymptotic Internal Path Length and the Asymptotic Wiener Index of Random Split Trees
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.
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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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