Probability Seminar

Rooted, weighted continuum random trees (CRTs) arise as scaling limits of random discrete trees with the uniform probability distribution on their vertices. Formally, these CRTs are random quadruples (T,d,r,p), where (T,d) is a random tree-like metric space, often a random fractal; r is a distinguished root vertex in T; and p a probability measure on T. We will discuss three related notions: exchangeable random hierarchies, i.e. nested partitions; a notion of "underlying tree structure" in rooted, weighted CRTs; and a novel family of such CRTs in which spacing in the trees is a function of the weight and underlying structure.