Journal of Applied Probability

Limit theorems for depths and distances in weighted random b-ary recursive trees

Götz Olaf Munsonius and Ludger Rüschendorf

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Abstract

Limit theorems are established for some functionals of the distances between two nodes in weighted random b-ary recursive trees. We consider the depth of the nth node and of a random node, the distance between two random nodes, the internal path length, and the Wiener index. As an application, these limit results imply, by an imbedding argument, corresponding limit theorems for further classes of random trees: plane-oriented recursive trees and random linear recursive trees.

Article information

Source
J. Appl. Probab. Volume 48, Number 4 (2011), 1060-1080.

Dates
First available: 16 December 2011

Permanent link to this document
http://projecteuclid.org/euclid.jap/1324046019

Digital Object Identifier
doi:10.1239/jap/1324046019

Zentralblatt MATH identifier
05994388

Mathematical Reviews number (MathSciNet)
MR2896668

Subjects
Primary: 05C05: Trees 60C05: Combinatorial probability 60F05: Central limit and other weak theorems

Keywords
Random tree Wiener index path length contraction method plane-oriented recursive tree

Citation

Munsonius, Götz Olaf; Rüschendorf, Ludger. Limit theorems for depths and distances in weighted random b -ary recursive trees. Journal of Applied Probability 48 (2011), no. 4, 1060--1080. doi:10.1239/jap/1324046019. http://projecteuclid.org/euclid.jap/1324046019.


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