Project Details
Projekt
Spatial population models with local self-interactions
Subject Area
Mathematics
Term
since 2020
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 443869423
We consider spatial population models with local (self-)interactions. The interaction can be induced by a common random (spatial) environment in which the individuals live (branching random walk in random environment). It can also be given by a local feed-back mechanism which regulates an individual's offspring law depending on the configuration in a certain neighbourhood around it. These models are more realistic than classical branching random walks, where particles move and branch completely independently. In the first case, they take into account inhomogeneities in the habitat. In the second case, they describe a self-regulation of the population coming for instance from a competition for resources. They are also harder to analyse: in the latter case, they are typically not "monotone" systems, since adding additional individuals at some time point can diminish the population at a later time. We focus on (1) extinction versus survival regimes, (2) the linear speed of the front, and the corresponding fluctuations, (3) genealogies and interfaces. A common connecting tool is the study of the spatial embedding of ancestral lines. They are random walks in a dynamic random environment, and the study of such random walks has an independent interest.
DFG Programme
Priority Programmes
Subproject of
SPP 2265:
Random geometric systems
International Connection
Switzerland
Partner Organisation
Schweizerischer Nationalfonds (SNF)
Cooperation Partner
Professor Dr. Jiri Cerny
