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

By Nicolas Broutin and Luc Devroye


We use large deviations to prove a general theorem on the asymptotic edge-weighted height H ⋆ n of a large class of random trees for which H ⋆ n ∼ 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 [11], [13], random recursive trees [12] and plane oriented trees [23] for instance. New applications include the heights of some random lopsided trees [19] and of the intersection of random trees

Topics: Probabilistic analysis, Large deviations
Publisher: Springer Science+Business Media, Inc.
Year: 2006
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
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