LA Probability Forum (2/3)

Given two independent uniform random trees on n vertices, what can be said about the size and shape of their largest common subtree? This problem belongs to the broad study of large common substructures, a topic that has recently seen growing interest in probability and combinatorics. In this talk, we answer that question by presenting a scaling limit for the size of the largest common subtree. Moreover, our approach extends to a more general setting: the same scaling limit holds for two independent critical Bienaymé--Galton--Watson trees with finite-variance offspring distributions, conditioned to have size n, under a mild (but necessary) assumption. The talk is based on joint work with Omer Angel, Caelan Atamanchuk, Anna Brandenberger, and Serte Donderwinkel.