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Asymptotic Properties of Protected Nodes in Random Recursive Trees

Part of: Limit theorems Combinatorial probability

Published online by Cambridge University Press:  30 January 2018

Hosam M. Mahmoud  and
Mark D. Ward
Hosam M. Mahmoud*
Affiliation:
The George Washington University
Mark D. Ward*
Affiliation:
Purdue University
*
∗ Postal address: Department of Statistics, The George Washington University, Washington, DC 20052, USA. Email address: hosam@gwu.edu
∗∗ Postal address: Department of Statistics, Purdue University, West Lafayette, IN 47907-2067, USA. Email address: mdw@purdue.edu
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Abstract

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We investigate protected nodes in random recursive trees. The exact mean of the number of such nodes is obtained by recurrence, and a linear asymptotic equivalent follows. A nonlinear recurrence for the variance shows that the variance grows linearly, too. It follows that the number of protected nodes in a random recursive tree, upon proper scaling, converges in probability to a constant.

Keywords

Recursive treerandom structurecombinatorial probability

MSC classification

Primary: 60C05: Combinatorial probability 60F05: Central limit and other weak theorems
Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 1 , March 2015 , pp. 290 - 297
Copyright
© Applied Probability Trust 

References

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