Interacting Fisher-Wright diffusions in a catalytic medium (Q5944098)

The authors study the long-time behaviour of interacting Fisher-Wright diffusions in a random 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. For both the processes, the local rates are assumed to be proportional to a random environment (catalytic medium), and the medium is chosen to be the case of nearest neighbour migration on the \(d\)-dimensional lattice. The authors prove that the models exhibit new phenomena compared with branching in catalytic media: in dimensions three or higher, the result is as usually expected; but in dimensions two and one, the long-time behaviour is quite different. The hardest case is dimension two.