Quantitative Large Population Limit for Non Exchangeable Diffusions in Fisher Information
Probability
2026-04-14 v1
Abstract
This paper builds upon the methods developed in [22] and [15] to investigate the large population behavior of non exchangeable systems of N diffusive particles when the interaction matrix converges (in some sense) to a graphon. We first prove that the particle system is well approximated in Fisher information by the so-called independent projection system by proving quantitative bounds on the relative Fisher information between the marginal laws of both systems. We then use a convenient equivalence between the independent projection system and a graphon mean field system to investigate its large population behavior by proving quantitative stability estimates for graphon mean field systems in both relative entropy and Fisher information.
Cite
@article{arxiv.2604.11385,
title = {Quantitative Large Population Limit for Non Exchangeable Diffusions in Fisher Information},
author = {Jules Grass},
journal= {arXiv preprint arXiv:2604.11385},
year = {2026}
}