## Journal of Applied Probability

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

### Asymptotic properties of protected nodes in random recursive trees

Hosam M. Mahmoud and Mark D. Ward

#### 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