Minmin Wang (University of Sussex) – Exchangeability in Continuum Random Trees

De Fenetti’s Theorem states that all N-indexed exchangeable sequences of real-valued random variables are mixings of i.i.d sequences. For real-valued random processes with exchangeable increments on [0, 1], Kallenberg’s 1973 result provides a complete characterisation of these processes via another mixing relationship. This talk is about an analogue of Kallenberg’s Theorem for random trees. We will explore the connection between random trees and stochastic processes, leading to a conjecture by Aldous, Miermont and Pitman on a mixing relationship of continuum random trees, and a recent proof of the conjecture.