P02
Spatial population models with local self-interactions
Description
We consider spatial population models with local (self-)interactions. The interaction can be either induced by a common random (spatial) environment in which the individuals live or it can be modelled explicitly 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; they are also harder to analyse because of this lack of independence and also because they typically
are not “monotone” systems, since adding additional individuals can be actually harmful for the present population.
We focus on (1) extinction versus survival regimes, (2) in an equilibrium, when including neutraltypes: growth of clusters versus local diversity, (3) front speed and fluctuations in expanding populations in a random environment. A common connecting tool is the study of the spatial embedding of ancestral lines, which are random walks in a dynamic random environment.
We focus on (1) extinction versus survival regimes, (2) in an equilibrium, when including neutraltypes: growth of clusters versus local diversity, (3) front speed and fluctuations in expanding populations in a random environment. A common connecting tool is the study of the spatial embedding of ancestral lines, which are random walks in a dynamic random environment.
Preprints/Publications
Stein Andreas Bethuelsen, Matthias Birkner, Andrej Depperschmidt, Timo Schlüter: Local limit theorems for a directed random walk on the backbone of a supercritical oriented percolation cluster (05/2021)
Members
-
Prof. Dr. Matthias Birkner
Johannes Gutenberg-Universität Mainz
Principal Investigator -
Prof. Dr. Nina Jael Gantert
Technische Universität München
Principal Investigator -
Dr. Alice Callegaro
Technische Universität München
Associated Scientist -
Prof. Dr. Jiří Černý
Universität Basel
Associated Scientist -
B. Sc. Gideon R. Chiusole
Technische Universität München
Associated Scientist -
M. Sc. Jan Lukas Igelbrink
Johannes Gutenberg-Universität Mainz
Associated Scientist -
M. Sc. Pascal Oswald
Universität Basel
Associated Scientist -
Dr. Guilherme Henrique de Paula Reis
Technische Universität München
Associated Scientist
