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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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

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

First available in Project Euclid: 16 December 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


Munsonius, Götz Olaf; Rüschendorf, Ludger. Limit theorems for depths and distances in weighted random b -ary recursive trees. J. Appl. Probab. 48 (2011), no. 4, 1060--1080. doi:10.1239/jap/1324046019.

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