Contraction of Rényi Divergences for Discrete Channels: Properties and Applications

Adrien Vandenbroucque; Amedeo Roberto Esposito; Michael Gastpar

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arXiv · 2601.09328

Contraction of Rényi Divergences for Discrete Channels: Properties and Applications

Adrien Vandenbroucque·Amedeo Roberto Esposito·Michael Gastpar

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Abstract

This work explores properties of Strong Data-Processing constants for Rényi Divergences. Parallels are made with the well-studied $φ$-Divergences, and it is shown that the order $α$ of Rényi Divergences dictates whether certain properties of the contraction of $φ$-Divergences are mirrored or not. In particular, we demonstrate that when $α>1$, the contraction properties can deviate quite strikingly from those of $φ$-Divergences. We also uncover specific characteristics of contraction for the $\infty$-Rényi Divergence and relate it to $\varepsilon$-Local Differential Privacy. The results are then applied to bound the speed of convergence of Markov chains, where we argue that the contraction of Rényi Divergences offers a new perspective on the contraction of $L^α$-norms commonly studied in the literature.

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Adrien Vandenbroucque, Amedeo Roberto Esposito, Michael Gastpar. 2026-01-14. Contraction of Rényi Divergences for Discrete Channels: Properties and Applications. https://arxiv.org/abs/2601.09328

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