Sharp propagation of chaos in R\'enyi divergence

Abstract

We establish sharp rates for propagation of chaos in R\'enyi 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 $\mathsf R_q(\mu^1 \,\lVert\, \pi) = \widetilde O(\frac{d q^2}{N^2})$ bounds on the $q$-R\'enyi divergence.