Propagation of chaos in Fisher information
Probability
2025-11-26 v1
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.
Keywords
Cite
@article{arxiv.2511.20078,
title = {Propagation of chaos in Fisher information},
author = {Jules Grass and Christophe Poquet and Arnaud Guillin},
journal= {arXiv preprint arXiv:2511.20078},
year = {2025}
}