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

@article{Gufler2016ARF,
  title={A representation for exchangeable coalescent trees and generalized tree-valued Fleming-Viot processes},
  author={Stephan Gufler},
  journal={arXiv: Probability},
  year={2016}
}
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… 
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References

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Pathwise construction of tree-valued Fleming-Viot processes

In a random complete and separable metric space that we call the lookdown space, we encode the genealogical distances between all individuals ever alive in a lookdown model with simultaneous multiple…

Convergence of tree-valued Cannings chains

We consider sequences of tree-valued Markov chains that describe evolving genealogies in Cannings models, and we show their convergence in distribution to tree-valued Fleming-Viot processes. Under…

Invariance principles for tree-valued Cannings chains

We consider sequences of tree-valued Markov chains that describe evolving genealogies in Cannings models, and we show their convergence in distribution to tree-valued Fleming-Viot processes. Under…

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The measure-valued Fleming–Viot process is a diffusion which models the evolution of allele frequencies in a multi-type population. In the neutral setting the Kingman coalescent is known to generate…

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