Sharp propagation of chaos in Rényi divergence

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 $\mathsf R_q(μ^1 ,\lVert, π) = \widetilde O(\frac{d q^2}{N^2})$ bounds on the $q$-Rényi divergence.

💡 Research Summary

The paper investigates the quantitative propagation of chaos for interacting diffusion systems at equilibrium, focusing on Rényi divergences rather than the more commonly studied Kullback–Leibler (KL) divergence or Wasserstein distances. The authors build on the entropic hierarchy introduced by Lacker (2023) and extend it to the family of Rényi‑q divergences defined by

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