Spatial growth and information exchange in evolving environments
and on evolving networks
What is the effect of the space-time varying environment on the long time behavior of spatially structured populations of interacting particles/individuals/agents? This question is of high relevance, e.g., in life and social sciences/economics, computer science, artificial intelligence. Mathematically, the project focuses on two phenomenological models of interacting particle systems: (1) branching Brownian motion, which models population growth/spatial spreading; and (2) voter model, which models information exchange in a population of agents. The novel features that this project introduces into these classical models are: (1) space-time-correlated environments and (2) evolving networks. These play the role of the geographic spaces and substantially change the underlying spatial geometry. The project aims at investigating (1) growth vs. extinction, population size, spread; and (2) clustering vs. consensus of agents, space-time scaling limits of stochastic processes on evolving networks and evolving graph limits.