We show that the number of copies of a given rooted tree in a conditioned Galton–Watson tree satisfies a law of large numbers under a minimal moment condition on the offspring distribution.
Supported by the Knut and Alice Wallenberg Foundation.
I thank Stephan Wagner and an anonymous referee for helpful comments.
"On general subtrees of a conditioned Galton–Watson tree." Electron. Commun. Probab. 26 1 - 12, 2021. https://doi.org/10.1214/21-ECP392