Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

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

Bo Chen and Matthias Winkel

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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.


Nous introduisons la notion d’une partition restreinte échangeable de $\mathbb{N}$. Nous obtenons des représentations intégrales, nous considérons les fragmentations associées, des plongements dans des arbres aléatoires continus et la convergence vers de tels arbres limites. En particulier, nous déduisons de la théorie générale développée içi un résultat limite formulé en conjecture dans un travail précédent. Ce résultat particulier concerne les arbres alpha de Ford et leurs généralisations, les arbres alpha-gamma, deux exemples où l’échangeabilité restreinte arrive de manière naturelle.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 49, Number 3 (2013), 839-872.

First available in Project Euclid: 2 July 2013

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Zentralblatt MATH identifier

Primary: 60G09: Exchangeability 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Exchangeability Hierarchy Coalescent Fragmentation Continuum random tree Renewal theory


Chen, Bo; Winkel, Matthias. Restricted exchangeable partitions and embedding of associated hierarchies in continuum random trees. Ann. Inst. H. Poincaré Probab. Statist. 49 (2013), no. 3, 839--872. doi:10.1214/12-AIHP533.

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