Bimodality and Phase Transitions in the Profile Variance of Random Binary Search Trees

  title={Bimodality and Phase Transitions in the Profile Variance of Random Binary Search Trees},
  author={Michael Drmota and Hsien-Kuei Hwang},
  journal={SIAM J. Discrete Math.},
We show that the variance of the profiles (number of nodes at each level) of random binary search trees exhibits asymptotically four phase transitions and a bimodal or “two-hump ed” behavior, in contrast to the unimodality of the mean value of the profiles. Precise asymptotic appr oximations are derived. The same types of phenomena also hold for the profiles of random recursive trees. 

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