Sharp propagation of chaos in Rényi divergence

Abstract

We establish sharp rates for propagation of chaos in Rényi divergences for interacting diffusion systems at stationarity. Building upon the entropic hierarchy established in Lacker (2023), we show that under strong isoperimetry and weak interaction conditions, one can achieve ${\mathsf{R}}_q({\mu }^1\Vert \pi )=\tilde{O}(\frac{d{q}^2}{N^2})$ bounds on the $q$-Rényi divergence.