Restricted exchangeable partitions and embedding of associated hierarchies in continuum random trees

Abstract

We introduce the notion of a restricted exchangeable partition of N and study natural classes of such partitions. We obtain integral representations, study associated coalescents and fragmentations, embeddings into continuum random trees and convergence to such limit trees. As an application, we deduce from the general theory developed here a particular limit result conjectured previously for Ford’s alpha model and its non-binary extension, the alpha-gamma model, where restricted exchangeability arises naturally. AMS 2000 subject classifications: 60G09, 60J80.