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Limit Theorems for Depths and Distances in Weighted Random B-Ary Recursive Trees

Part of: Combinatorial probability Limit theorems Graph theory

Published online by Cambridge University Press:  14 July 2016

Götz Olaf Munsonius  and
Ludger Rüschendorf
Götz Olaf Munsonius*
Affiliation:
University of Freiburg
Ludger Rüschendorf*
Affiliation:
University of Freiburg
*
∗ Current address: Institute of Mathematics, University of Frankfurt, 60054 Frankfurt am Main, Germany. Email address: munsonius@math.uni-frankfurt.de
∗∗ Postal address: Department of Mathematical Stochastics, University of Freiburg, Eckerstraße 1, 79104 Freiburg, Germany. Email address: ruschen@stochastik.uni-freiburg.de
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Abstract

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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.

Keywords

Random treeWiener indexpath lengthcontraction methodplane-oriented recursive tree

MSC classification

Secondary: 05C05: Trees 60C05: Combinatorial probability 60F05: Central limit and other weak theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 4 , December 2011 , pp. 1060 - 1080
Copyright
Copyright © Applied Probability Trust 2011 

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