Interacting Fisher-Wright Diffusions in a Catalytic Medium
Klenke A, Wakolbinger A, Greven A (2001)
Publication Type: Journal article
Publication year: 2001
Journal
Publisher: Springer Verlag (Germany)
Book Volume: 120
Pages Range: 85-117
Journal Issue: 1
URI: https://link.springer.com/article/10.1007/PL00008777
DOI: 10.1007/PL00008777
Abstract
We study the longtime behaviour of interacting systems in a randomly fluctuating (space-time) medium and focus on models from population genetics. There are two prototypes of spatial models in population genetics: spatial branching processes and interacting Fisher-Wright diffusions. Quite a bit is known on spatial branching processes where the local branching rate is proportional to a random environment (catalytic medium). Here we introduce a model of interacting Fisher-Wright diffusions where the local resampling rate (or genetic drift) is proportional to a catalytic medium. For a particular choice of the medium, we investigate the longtime behaviour in the case of nearest neighbour migration on the d-dimensional lattice. While in classical homogeneous systems the longtime behaviour exhibits a dichotomy along the transience/recurrence properties of the migration, now a more complicated behaviour arises. It turns out that resampling models in catalytic media show phenomena that are new even compared with branching in catalytic medium.
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APA:
Klenke, A., Wakolbinger, A., & Greven, A. (2001). Interacting Fisher-Wright Diffusions in a Catalytic Medium. Probability Theory and Related Fields, 120(1), 85-117. https://dx.doi.org/10.1007/PL00008777
MLA:
Klenke, Achim, Anton Wakolbinger, and Andreas Greven. "Interacting Fisher-Wright Diffusions in a Catalytic Medium." Probability Theory and Related Fields 120.1 (2001): 85-117.
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