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2018 A representation for exchangeable coalescent trees and generalized tree-valued Fleming-Viot processes
Stephan Gufler
Electron. J. Probab. 23: 1-42 (2018). DOI: 10.1214/18-EJP153

Abstract

We give a de Finetti type representation for exchangeable random coalescent trees (formally described as semi-ultrametrics) in terms of sampling iid sequences from marked metric measure spaces. We apply this representation to define versions of tree-valued Fleming-Viot processes from a $\Xi $-lookdown model. As state spaces for these processes, we use, besides the space of isomorphy classes of metric measure spaces, also the space of isomorphy classes of marked metric measure spaces and a space of distance matrix distributions. This allows to include the case with dust in which the genealogical trees have isolated leaves.

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Stephan Gufler. "A representation for exchangeable coalescent trees and generalized tree-valued Fleming-Viot processes." Electron. J. Probab. 23 1 - 42, 2018. https://doi.org/10.1214/18-EJP153

Information

Received: 15 October 2016; Accepted: 24 February 2018; Published: 2018
First available in Project Euclid: 9 May 2018

zbMATH: 1390.60125
MathSciNet: MR3806409
Digital Object Identifier: 10.1214/18-EJP153

Subjects:
Primary: 60G09
Secondary: 60J25 , 60K35 , 92D10

Keywords: $\Xi $-coalescent , dust , jointly exchangeable array , lookdown model , marked metric measure space , tree-valued Fleming-Viot process , ‎ultrametric

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