Quantitative propagation of chaos for non-exchangeable diffusions via first-passage percolation

TL;DR

This paper introduces a non-asymptotic method for analyzing mean field approximations in non-exchangeable diffusive particle systems, leveraging a novel connection with first-passage percolation to derive sharp entropy bounds.

Contribution

It extends mean field approximation techniques to non-exchangeable systems using a hierarchy of entropy inequalities and a new link to first-passage percolation.

Findings

Sharp relative entropy estimates for non-exchangeable diffusions.

A hierarchy of differential inequalities for entropy bounds.

A novel connection between particle systems and first-passage percolation.

Abstract

This paper develops a non-asymptotic approach to mean field approximations for systems of $n$ diffusive particles interacting pairwise. The interaction strengths are not identical, making the particle system non-exchangeable. The marginal law of any subset of particles is compared to a suitably chosen product measure, and we find sharp relative entropy estimates between the two. Building upon prior work of the first author in the exchangeable setting, we use a generalized form of the BBGKY hierarchy to derive a hierarchy of differential inequalities for the relative entropies. Our analysis of this complicated hierarchy exploits an unexpected but crucial connection with first-passage percolation, which lets us bound the marginal entropies in terms of expectations of functionals of this percolation process.