On the asymptotic internal path length and the asymptotic Wiener index of random split trees

Details On the asymptotic internal path length and the asymptotic Wiener index of random split trees On the asymptotic internal path length and the asymptotic Wiener index of random split trees

2011-01-13

arxiv.org/abs/1101.2570v3

Electron. J. Probab. 16 (2011), 1020-1047

Mathematics

Probability

29 pages

Scientific paper

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.

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