In this project, I plan to work with Prof. F. den Hollander on extending the renormalization analysis of Dawson and Greven and den Hollander et al. for hierarchically interacting diffusions from linear drift to nonlinear drift. The goal is to find a suitable renormalization scheme and to identify the corresponding universality classes for the large space-time scale behaviour.
Such an extension will reveal rich new phenomena and will shed light on the evolution of a large class of population genetics models. In particular, it will allow us to understand how sensitive the evolution on the macroscopic scale is to the details of the microscopic interactions.
Call for proposal
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