Mean-field limits \`a la Tanaka and large deviations for particle systems with network interactions

This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms.

The starting point is a fixed-point formulation of particle systems originally due to Tanaka that allows us to prove mean-field limit and large deviation results in an abstract setting.

While it has been recently shown that such formulation encompasses a large class of exchangeable particle systems, we propose here a setting for the non-exchangeable case, including the case of adaptive interaction networks.

We introduce sufficient conditions on the network structure that imply the mean-field limit and a new large deviations principle for the interaction measure.

Finally, we formally highlight important models for which it is possible to derive a closed PDE characterization of the limit.