Genealogical aspects of symbiotic and mutually catalytic branching processes

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In the first period of the priority programme 1590, our PhD student Fridolin Kielisch has established a genealogical construction for mutually catalytic branching processes (both on the particle level and in the continuous masses limit) as well as for the symbiotic branching process (on the particle level). This construction is in the spirit of the lookdown constructions of Donnelly and Kurtz and more recently by Kurtz and Rodrigues. The next goal is to obtain a similar construction also for the continuous masses symbiotic branching process. This would finish the PhD thesis.Furthermore, for these models, the limit of the lookdown processes as the branching rate tends to infinity shall be studied. While primarily the goal is to reach a deeper understanding of the genealogies of symbiotic branching processes, we also hope to get some new insight in the renormalization analysis of the infinite rate processes. This would stress the special role of symbiotic branching processes.