A representation for exchangeable coalescent trees and generalized tree-valued Fleming-Viot processes
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 -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.
Cite
@article{arxiv.1608.08074,
title = {A representation for exchangeable coalescent trees and generalized tree-valued Fleming-Viot processes},
author = {Stephan Gufler},
journal= {arXiv preprint arXiv:1608.08074},
year = {2017}
}
Comments
49 pages. The organization is modified. Remark 1.1 and the proof of Proposition 3.17 (which is Corollary 3.25 in v2) are corrected. The third proof of Proposition 3.16 from v2 is removed due to a measurability issue that does not affect the other proofs. Since v1, this paper includes some parts that have been split off from arXiv:1404.3682v2