Title: A few central limit theorems for critical beta-splitting trees
Abstract: The critical beta-splitting tree is a random tree, originally proposed by Aldous as a toy model for phylogenetic trees, which has recently attracted renewed mathematical interest. In this talk, I will introduce the model, mention some of its unique properties, and discuss recent work in which we prove central limit theorems for various statistics of the tree. This confirms conjectures of Aldous, Janson, and Pittel. The proofs rely on a precise asymptotic analysis combined with a variant of the contraction method for distributional recursions. This is joint work with Anna Brandenberger and Elchanan Mossel.