24.11.2025 15:00 Christian Fiedler:
Mean-field limits for discrete-time dynamical systems via kernel mean embeddingMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

Mean field limits are an important tool in the context of large-scale dynamical systems, in particular, when studying multiagent and interacting particle systems. While the continuous-time theory is well-developed, few works have considered mean field limits for deterministic discrete-time systems, which are relevant for the analysis and control of large-scale discrete-time multiagent system. We prove existence results for the mean field limit of very general discrete-time dynamical systems, which in particular encompass typical multiagent systems. As a technical novelty, we utilize kernel mean embeddings, which are an established tool in machine learning and statistics, but have been rarely used in the context of multiagent systems and kinetic theory. Our results can serve as a rigorous foundation for many applications of mean field approaches for discrete-time dynamical systems, from analysis, simulation and control to learning.