Non-fringe subtrees in conditioned Galton--Watson trees

Abstract

We study $S({\mathcal{T}}_n)$, the number of subtrees in a conditioned Galton--Watson tree of size $n$. With two very different methods, we show that $\log (S({\mathcal{T}}_n))$ has a Central Limit Law and that the moments of $S({\mathcal{T}}_n)$ are of exponential scale.