State Dependent Multitype Spatial Branching
This talk will describe joint work with Andreas Greven on spatial infinite type branching systems indexed by a countable group, for example $Z^d$ or the hierarchical group. The space of types is [0,1] and the state of the system at a given site is a measure on [0,1]. The spatial components of the system interact via migration. Instead of the classical independence assumption on the evolution of different families of the branching population, we introduce interaction between the families through a state dependent branching rate of individuals and state dependent mean offspring of individuals but for most results we restrict attention to the critical case. One objective is to establish that the large scale structure of surviving types is related to the immortal clan of super-Brownian motion.