Exchangeability, mixtures and continuum random trees

I’ll start with a quick review on some classical results on exchangeability, particularly Kallenberg’s theorem on the canonical form of an exchangeable process on [0, 1]. The 2005 work of Aldous, Miermont and Pitman reveals a close connection between exchangeable processes and a class of continuum random tree called inhomogeneous continuum random trees (ICRT), leading to their claim that Lévy trees are mixtures of ICRT. I’ll present a proof in the case of stable Lévy trees, based upon a new way of constructing continuum random trees that work both for stable trees and ICRT.