Branching random walks in random environment are diffusive in the regular growth phase. (English) Zbl 1244.60100
Summary: We treat branching random walks in random environment using the framework of Linear Stochastic Evolution. In spatial dimensions three or larger, we establish diusive behaviour in the entire growth phase. This can be seen through a Central Limit Theorem with respect to the population density as well as through an invariance principle for a path measure we introduce.
MSC:
60K37 | Processes in random environments |
60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
60F17 | Functional limit theorems; invariance principles |
60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
82D30 | Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) |