Journal of Applied Probability

Asymptotic properties of protected nodes in random recursive trees

Hosam M. Mahmoud and Mark D. Ward

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 17 April 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Recursive tree random structure combinatorial probability


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.

Export citation