On the total heights of random rooted trees

On the total heights of random rooted trees

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Article ID: iaor1994248
Country: Israel
Volume: 29
Issue: 3
Start Page Number: 543
End Page Number: 556
Publication Date: Sep 1992
Journal: Journal of Applied Probability
Authors:
Keywords: statistics: distributions
Abstract:

Denote by Sn the set of all distinct rooted trees with n labeled vertices. Define τn as the total height of a tree chosen at random in the set Sn, assuming that all the possible nn’-1 choices are equally probable. The total height of a tree is defined as the sum of the heights of its vertices. The height of a vertex in a rooted tree is the distance from the vertex to the root of the tree, that is, the number of edges in the path from the vertex to the root. This paper is concerned with the distribution and the moments of τn and their asymptotic behavior as n⇒•.

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