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

Abstract

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.