Electronic Journal of Probability

A representation for exchangeable coalescent trees and generalized tree-valued Fleming-Viot processes

Stephan Gufler

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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.

Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 41, 42 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1525852818

Digital Object Identifier
doi:10.1214/18-EJP153

Mathematical Reviews number (MathSciNet)
MR3806409

Zentralblatt MATH identifier
1390.60125

Subjects
Primary: 60G09: Exchangeability
Secondary: 60J25: Continuous-time Markov processes on general state spaces 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 92D10: Genetics {For genetic algebras, see 17D92}

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

Gufler, Stephan. A representation for exchangeable coalescent trees and generalized tree-valued Fleming-Viot processes. Electron. J. Probab. 23 (2018), paper no. 41, 42 pp. doi:10.1214/18-EJP153. https://projecteuclid.org/euclid.ejp/1525852818


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