General Edgeworth expansions with applications to profiles of random trees

@article{Kabluchko2016GeneralEE,
  title={General Edgeworth expansions with applications to profiles of random trees},
  author={Zakhar Kabluchko and Alexander Marynych and Henning Sulzbach},
  journal={arXiv: Probability},
  year={2016},
  pages={3478-3524}
}
  • Zakhar Kabluchko, Alexander Marynych, Henning Sulzbach
  • Published 2016
  • Mathematics
  • arXiv: Probability
  • We prove an asymptotic Edgeworth expansion for the profiles of certain random trees including binary search trees, random recursive trees and plane-oriented random trees, as the size of the tree goes to infinity. All these models can be seen as special cases of the one-split branching random walk for which we also provide an Edgeworth expansion. These expansions lead to new results on mode, width and occupation numbers of the trees, settling several open problems raised in Devroye and Hwang… CONTINUE READING

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