Propagation of chaos in Fisher information

TL;DR

This paper introduces a novel method to establish sharp local propagation of chaos in Fisher Information for particle systems with smooth interactions, extending previous work and demonstrating optimal decay rates.

Contribution

The authors develop a new approach using a lemma on Fisher Information and the BBGKY hierarchy to prove propagation of chaos in Fisher Information, generalizing prior results.

Findings

New method for sharp local propagation of chaos in Fisher Information

Generalization of Lacker's work using BBGKY hierarchy

Optimal decay rate demonstrated with Gaussian example

Abstract

We present a new method for proving sharp local propagation of chaos in Fisher Information for particles with smooth interaction and drift. We rely on a new Lemma computing the Fisher Information of two diffusion processes with smooth drifts and fine estimates on the hessian of the law of the solution of the McKean-Vlasov equation. It allows us to obtain a new propagation of chaos in Fisher information, generalizing Lacker's seminal work by using the BBGKY hierarchy to obtain a system of differential inequalities satisfied by both the relative entropy and the Fisher Information of k particles. We also show with a simple Gaussian example that our decay rate is optimal.