The asymptotic distribution of leaf heights in binary trees
type: Item
instance of: scholarly article
title: The asymptotic distribution of leaf heights in binary trees
zbMATH Open document ID: 0772.05034
DOI: 10.1007/BF02349961
published in: Graphs and Combinatorics
publication date: 1993-01-16T00:00:00Z
review text: The height \(h_ t(i)\) of the \(i\)-th leaf (counted from left to right) in a tree \(t\) is the distance from the root to this leaf. This paper derives the asymptotic distribution of the normalized height \(h_ t(i)/\sqrt n\) as \(i/n\to x\), in a random tree with \(n\) internal nodes. This distribution is shown to be a Maxwell distribution, the distribution of the square root of a sum of squares of independent normally distributed random variables.
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C80
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 93440
zbMATH Keywords: height
zbMATH Keywords: asymptotic distribution
zbMATH Keywords: random tree
Wikidata QID: Q59255191
author: Walter J. Gutjahr
author: Georg Ch. Pflug
reviewed by: Alan C. Tucker
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 93440