A framework for deriving R\'enyi entropy-power inequalities (EPIs) is presented that uses linearization and an inequality of Dembo, Cover, and Thomas. Simple arguments are given to recover the previously known R\'enyi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent $\alpha$ of previous works. An information-theoretic proof of the Dembo-Cover-Thomas inequality---equivalent to Young's convolutional inequality with optimal constants---is provided, based on properties of R\'enyi conditional and relative entropies and using transportation arguments from Gaussian densities. For log-concave densities, a transportation proof of a sharp varentropy bound is presented.

中文翻译：

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R\'enyi 熵功率和正常输运

提出了用于推导 R\'enyi 熵-幂不等式 (EPI) 的框架，该框架使用线性化和 Dembo、Cover 和 Thomas 的不等式。通过统一具有常数 c 的乘法形式和具有先前作品的指数 $\alpha$ 的修改，给出了简单的参数来恢复先前已知的 R\'enyi EPI 并推导出新的 EPI。基于 R\'enyi 条件熵和相对熵的性质，并使用来自高斯密度的传输参数，提供了 Dembo-Cover-Thomas 不等式的信息论证明——等效于具有最佳常数的杨氏卷积不等式。对于对数凹密度，给出了锐变熵界的传输证明。