Limit theorems for random trees.
Lea Takács · Proceedings of the National Academy of Sciences · 1992
This paper is concerned with random rooted trees and studies the distribution of the vertices according to their altitude. If the trees are chosen at random with an increasing number of vertices, then, by a suitable normalization, the distribution function of the number of vertices at a given altitude and the distribution function of the total height approach specific limits. Explicit formulas are given for these limit distribution functions and their moments.