Journal of Applied Probability

Asymptotic properties of protected nodes in random recursive trees

Hosam M. Mahmoud and Mark D. Ward

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Abstract

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.

Article information

Source
J. Appl. Probab., Volume 52, Number 1 (2015), 290-297.

Dates
First available in Project Euclid: 17 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.jap/1429282623

Digital Object Identifier
doi:10.1239/jap/1429282623

Mathematical Reviews number (MathSciNet)
MR3336863

Zentralblatt MATH identifier
1289.93055

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

Keywords
Recursive tree random structure combinatorial probability

Citation

Mahmoud, Hosam M.; Ward, Mark D. Asymptotic properties of protected nodes in random recursive trees. J. Appl. Probab. 52 (2015), no. 1, 290--297. doi:10.1239/jap/1429282623. https://projecteuclid.org/euclid.jap/1429282623


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