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On the entropy power inequality for the Renyi entropy of order [0,1]

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 Added by James Melbourne
 Publication date 2017
and research's language is English




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Using a sharp version of the reverse Young inequality, and a Renyi entropy comparison result due to Fradelizi, Madiman, and Wang, the authors are able to derive Renyi entropy power inequalities for log-concave random vectors when Renyi parameters belong to $(0,1)$. Furthermore, the estimates are shown to be sharp up to absolute constants.



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77 - Eshed Ram , Igal Sason 2016
This paper gives improved R{e}nyi entropy power inequalities (R-EPIs). Consider a sum $S_n = sum_{k=1}^n X_k$ of $n$ independent continuous random vectors taking values on $mathbb{R}^d$, and let $alpha in [1, infty]$. An R-EPI provides a lower bound on the order-$alpha$ Renyi entropy power of $S_n$ that, up to a multiplicative constant (which may depend in general on $n, alpha, d$), is equal to the sum of the order-$alpha$ Renyi entropy powers of the $n$ random vectors ${X_k}_{k=1}^n$. For $alpha=1$, the R-EPI coincides with the well-known entropy power inequality by Shannon. The first improved R-EPI is obtained by tightening the recent R-EPI by Bobkov and Chistyakov which relies on the sharpened Youngs inequality. A further improvement of the R-EPI also relies on convex optimization and results on rank-one modification of a real-valued diagonal matrix.
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