Profiles of random trees: Plane-oriented recursive trees
Random Structures & Algorithms
The shape of unlabeled rooted random trees
European Journal of Combinatorics
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We show that the variances of the profile (number of nodes at each level) of random binary search trees undergoes asymptotically four phase transitions and exhibits a bimodal or "two-humped" behavior, in contrast to the unimodality of the expected value of the profiles. Precise asymptotic approximations are derived. The same types of phenomena also hold for the profile of random recursive trees.