HISOCS · Hierarchical self-organisation in complex stochastic systems

The proposed research project aims at a rigorous mathematical understanding of the emergence of universal hierarchical structures and of the phenomenon of hierarchical self-organization for paradigmatic stochastic models of complex systems that involve long- and short-range interactions. For this purpose, we shall employ recent breakthroughs in understanding of multiple space-time scale collective behaviour of interacting spatio-temporal random systems. Moreover, we shall employ techniques and objects that were recently identified in the context of mathematical analysis of disordered systems. This understanding will allow us to identify the main governing parameters of the stochastic models that, in turn, will allow us to calibrate the models and to suggest ways to control real-world complex systems.