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


 
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1. Title Title of document On the Asymptotic Internal Path Length and the Asymptotic Wiener Index of Random Split Trees
 
2. Creator Author's name, affiliation, country Goetz Olaf Munsonius; University of Frankfurt; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) random trees; probabilistic analysis of algorithms; internal path length; Wiener index
 
3. Subject Subject classification 60F05; 68P05; 05C05
 
4. Description Abstract 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2011-06-01
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/889
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-889
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
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