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.
Citation
Hosam M. Mahmoud. Mark D. Ward. "Asymptotic properties of protected nodes in random recursive trees." J. Appl. Probab. 52 (1) 290 - 297, March 2015. https://doi.org/10.1239/jap/1429282623
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