Renormalization of genealogies of spatial population models

点击翻译按钮获取中文摘要

The project develops the stochastic analysis of processes of evolving genealogies modelled as Feller or Fleming-Viot processes respectively their spatial versions, respectively versions where we add driffterms reflecting limited resources. The genealogy is modelled as marked ultrametric probability space and the stochastic processes are defined ass solutions to wellposed martingale problems. The longtime behaviour and their universal properties are studied via renormalization and via the hierarchical meanfield limit in order to obtain the universality classes for these models. The continuation of the project focusses on catalytic branching, spatial continuum limits and logistic branching processes.