## Journal of Applied Probability

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

#### 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 in Project Euclid: 16 December 2011

http://projecteuclid.org/euclid.jap/1324046019

Digital Object Identifier
doi:10.1239/jap/1324046019

Zentralblatt MATH identifier
05994388

Mathematical Reviews number (MathSciNet)
MR2896668

#### 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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