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Asymptotic properties of protected nodes in random recursive trees. (English) Zbl 1397.60021

Summary: 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.

MSC:

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