The spatial Lambda-Fleming-Viot process: an event-based construction and a lookdown representation

@article{Vber2012TheSL,
  title={The spatial Lambda-Fleming-Viot process: an event-based construction and a lookdown representation},
  author={Amandine V{\'e}ber and A. Wakolbinger},
  journal={arXiv: Probability},
  year={2012}
}
We construct a measure-valued equivalent to the spatial Lambda-Fleming-Viot process (SLFV) introduced in [Eth08]. In contrast with the construction carried out in [Eth08], we fix the realization of the sequence of reproduction events and obtain a quenched evolution of the local genetic diversities. To this end, we use a particle representation which highlights the role of the genealogies in the attribution of types (or alleles) to the individuals of the population. This construction also… 

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