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

Abstract

We introduce the notion of a restricted exchangeable partition of N.We obtain integral representations, consider associated fragmentations, embeddings into continuum random trees and convergence to such limit trees. In particular, we deduce from the general theory developed here a limit result conjectured previously for Ford's alpha model and its extension, the alpha-gamma model, where restricted exchangeability arises naturally. © Association des Publications de l'Institut Henri Poincaré, 2013.