Scaling properties of a random Yule tree embedded in ${\mathbb{R}}^{\mathfrak{D}}$

Abstract

We study a random tree, which was introduced by Ajazi et al. as part of a model of a neuronal network. Realising a scaling relation for the law of the tree, we can use elementary techniques to derive asymptotic results on the geometry as time goes to infinity.

18 pages, 3 figures. Final version, to appear in Markov Processes and Related Fields