EF45 – Multi-Agent Social Systems



Concentration Effects and Collective Variables in Agent-Based Systems

Project Heads

Jobst Heitzig, Péter Koltai, Nora Molkenthin, Stefanie Winkelmann

Project Members

Marvin Lücke

Project Duration

01.02.2021 − 31.01.2024

Located at



Agent-based models (ABMs) are often high-dimensional and complex, making simulations costly and formal analysis hard. Low-dimensional model reduction is hence of great interest. The systems often show a “tightness”: the complex microdynamics of the O(N) many attributes of the individual agents can be approximated by the stochastic evolution of a small number (that is independent of N) of macroscopic collective variables describing the effective dynamics of the system. Moreover, if the number N of agents is large, one can observe a concentration of measure in the sense that the collective variables follow an almost deterministic and smooth evolution. In simple examples, suitable collective variables and approximate ODEs or SDEs governing the effective dynamics can be guessed or derived easily.


We formalize the efficacy of macroscopic modeling of ABMs by showing concentration of the process’ stochastic law transversal to low-dimensional coordinates of the full state. Further, we harness this property to numerically compute corresponding variables for systems where their analytical derivation is out of reach.


Marvin Lücke, Jobst Heitzig, Péter Koltai, Nora Molkenthin and Stefanie Winkelmann. “Large population limits of Markov processes on random networks”, Stochastic Processes and their Applications, 2023.

Marvin Lücke, Stefanie Winkelmann, Jobst Heitzig, Nora Molkenthin, Péter Koltai. “Learning interpretable collective variables for spreading processes on networks”, Physical Review E, 2024.

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