Mean-field limits \`a la Tanaka and large deviations for particle systems with network interactions
Abstract
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.
Cite
@article{arxiv.2510.04894,
title = {Mean-field limits \`a la Tanaka and large deviations for particle systems with network interactions},
author = {Louis-Pierre Chaintron and Antoine Diez},
journal= {arXiv preprint arXiv:2510.04894},
year = {2025}
}