Universality in Network Dynamics
~~One of the major achievements of statistical mechanics is the development of theoretical tools to bridge between the microscopic description of a system and its observed macroscopic behavior, tracking the emergence of large-scale phenomena from the mechanistic description of the system’s interacting components. A key factor in determining this emergent behavior is associated with the underlying geometry of the system’s interactions - a natural notion when treating structured systems, yet difficult to generalize when approaching complex systems. Indeed, social, biological and technological systems feature highly random and non-localized interaction patterns, which challenge the classical connection between structure, dimensionality and dynamics, and hence confront us with a potentially new class of dynamical behaviors. To observe these behaviors we developed a perturbative formalism that enables us to predict an array of pertinent macroscopic functions directly form the microscopic model describing the system’s dynamics. We find that while microscopically complex systems follow diverse rules of interaction, their macroscopic behavior condenses into a discrete set of dynamical universality classes.
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