Large Deviations for the Weighted Height of an Extended Class of Trees

  title={Large Deviations for the Weighted Height of an Extended Class of Trees},
  author={Nicolas Broutin and Luc Devroye},
We use large deviations to prove a general theorem on the asymptotic edge-weighted height Hn* of a large class of random trees for which Hn* ∼ c log n for some positive constant c. A graphical interpretation is also given for the limit constant c. This unifies what was already known for binary search trees, random recursive trees and plane oriented trees for instance. New applications include the heights of some random lopsided trees and of the intersection of random trees. 


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Showing 1-10 of 31 references

Branching processes and their application in the analysis of tree structures and tree algorithms

  • L. Devroye
  • M. Habib, C. McDiarmid, J. Ramirez-Alfonsin, and…
  • 1998
Highly Influential
20 Excerpts

Branching Processes

  • K. B. Athreya, P. E. Ney
  • Springer, Berlin
  • 1972
Highly Influential
5 Excerpts

The asymptotic shape of the branching random walk

  • J. D. Biggins
  • Advanced Applied Probability, 10:62–84
  • 1978
Highly Influential
6 Excerpts

Chernoff’s theorem in the branching random walk

  • J. D. Biggins
  • Journal of Applied Probability, 14:630–636
  • 1977
Highly Influential
6 Excerpts

Probability and Random Processes

  • G. R. Grimmett, D. R. Stirzaker
  • second edition. Oxford University Press, Oxford
  • 2001
3 Excerpts

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