Quantitative Large Population Limit for Non Exchangeable Diffusions in Fisher Information

TL;DR

This paper analyzes the large population limit of non-exchangeable diffusive particle systems interacting via a graphon, providing quantitative bounds and stability results in Fisher information and entropy.

Contribution

It extends methods to non-exchangeable systems, establishing Fisher information approximation and stability estimates for graphon-based mean field limits.

Findings

Particle system approximated by independent projection system in Fisher information

Quantitative bounds on relative Fisher information between systems

Stability estimates for graphon mean field systems in entropy and Fisher information

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.