Mathematical Sciences: Interacting Superprocesses

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The principal investigator will study interacting super- Brownian motions. Super-Brownian motion is a measure-valued diffusion that arises as a high density limit for a population of particles evolving in such a way that the total number of particles grows as a critical, continuous-time, Galton-Watson branching process, whilst in between births/deaths the particles move as independent Brownian motions. The goal of this research is to construct similar models for two populations which incorporate localized interaction terms. The import of these extra terms is to capture competition effects in which the presence of individuals from one population adversely affects the chance for individuals from the other population to successfully replicate themselves.