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

Bo Chen; Matthias Winkel

Annales de l'I.H.P. Probabilités et statistiques (2013)

  • Volume: 49, Issue: 3, page 839-872
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Chen, Bo, and Winkel, Matthias. "Restricted exchangeable partitions and embedding of associated hierarchies in continuum random trees." Annales de l'I.H.P. Probabilités et statistiques 49.3 (2013): 839-872. <http://eudml.org/doc/271978>.

@article{Chen2013,
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.},
author = {Chen, Bo, Winkel, Matthias},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {exchangeability; hierarchy; coalescent; fragmentation; continuum random tree; renewal theory},
language = {eng},
number = {3},
pages = {839-872},
publisher = {Gauthier-Villars},
title = {Restricted exchangeable partitions and embedding of associated hierarchies in continuum random trees},
url = {http://eudml.org/doc/271978},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Chen, Bo
AU - Winkel, Matthias
TI - Restricted exchangeable partitions and embedding of associated hierarchies in continuum random trees
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2013
PB - Gauthier-Villars
VL - 49
IS - 3
SP - 839
EP - 872
AB - 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.
LA - eng
KW - exchangeability; hierarchy; coalescent; fragmentation; continuum random tree; renewal theory
UR - http://eudml.org/doc/271978
ER -

References

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