The asymptotic distribution of leaf heights in binary trees (Q1199121)

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.