A central limit theorem for a spatial logistic branching process in the slow coalescence regime

Abstract: We study the scaling limits of a spatial population dynamics model which describes the sizes of colonies located on the integer lattice, and allows for branching, coalescence in the form of local pairwise competition, and migration. When started near the local equilibrium, the rates of branching and coalescence in the particle system are both linear in the local population size - we say that the coalescence is slow. We identify a rescaling of the equilibrium fluctuations process under which it converges to an infinite dimensional Ornstein-Uhlenbeck process with alpha-stable driving noise if the offspring distribution lies in the domain of attraction of an alpha-stable law with alpha between one and two.

analysis of PDEsclassical analysis and ODEsfunctional analysisprobabilityspectral theory

Audience: researchers in the discipline

Quebec Analysis and Related Fields Graduate Seminar