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

Abstract

We introduce the notion of a restricted exchangeable partition of $\mathbb{N}$. 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.

35 pages, 5 figures

References in corpus (4)

• Asymptotic laws for compositions derived from transformed subordinators
• Spinal partitions and invariance under re-rooting of continuum random trees
• Gibbs fragmentation trees
• Constrained exchangeable partitions