Mean-field limits for stochastic particle systems on dense graphs

Angeliki Koutsimpela; Elena Magnanini

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arXiv · 2606.11369

Mean-field limits for stochastic particle systems on dense graphs

Angeliki Koutsimpela·Elena Magnanini

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Abstract

We study stochastic interacting particle systems whose interaction structure is described by dense weighted directed graphs converging to a graphon. In the thermodynamic limit, we prove a law of large numbers for the empirical measure process and derive a deterministic nonlinear master equation describing the macroscopic evolution. The limiting equation retains the heterogeneous interaction structure of the microscopic system through the limiting graphon, allowing for spatially non-homogeneous behaviors such as localized or community-type interactions.

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Angeliki Koutsimpela, Elena Magnanini. 2026-06-09. Mean-field limits for stochastic particle systems on dense graphs. https://arxiv.org/abs/2606.11369

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