Stochastic models of inhomogeneous complex systems : Emergence of multi-scale hierarchies
In complex systems, a large number of elements interact via the network of interactions. However, the emerging collective behavior of the system cannot easily be inferred from that of the few individual components. We focus on several paradigmatic stochastic models of complex systems with inhomogeneous interactions. The models come from the following two classes: (a) "Energy-based", where the system searches for an energetically favorable state in a high-dimensional rugged „energy“ landscape; (b) "Information-based", where the system‘s elements evolve their individual states by exchanging information with their neighbors locally or across the network. We address the following questions. What is the emergent collective behavior in the stochastic models of complex systems on different scales of observation? What is the effect of the inhomogeneities on the behavior of the models? We identify the hierarchical structures which describe the space-time multi-scale behavior of the models. We study critical phenomena, fluctuations, and explore the universality classes of the models.