Interacting Fisher-Wright diffusions in a catalytic medium

• 成果类型: Article
• 署名作者: Greven, A; Klenke, A; Wakolbinger, A
• 署名单位: University of Erlangen Nuremberg; Goethe University Frankfurt
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/PL00008777
• 发表日期: 2001
• 页码: 85-117
• 关键词: ergodic-theorems; infinite systems; brownian-motion; BEHAVIOR; field

摘要

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.