Contraction of Rényi Divergences for Discrete Channels: Properties and Applications
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911376025321472 |
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| author | Vandenbroucque, Adrien Esposito, Amedeo Roberto Gastpar, Michael |
| author_facet | Vandenbroucque, Adrien Esposito, Amedeo Roberto Gastpar, Michael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09328 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Contraction of Rényi Divergences for Discrete Channels: Properties and Applications Vandenbroucque, Adrien Esposito, Amedeo Roberto Gastpar, Michael Information Theory Probability 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. |
| title | Contraction of Rényi Divergences for Discrete Channels: Properties and Applications |
| topic | Information Theory Probability |
| url | https://arxiv.org/abs/2601.09328 |