On the number of leaves in a random recursive tree

Abstract

This paper studies the asymptotic behavior of the number of leaves $L_{n}$ in a random recursive tree $T_{n}$ with $n$ nodes. By utilizing the size-bias method, we derive an upper bound on the Wasserstein distance between the distribution of $L_{n}$ and a standard normal distribution. Furthermore, we obtain a weak version of an Erdös–Rényi type law and a large deviation principle for $L_{n}$.