正态迁移和转动下的Rényi熵幂不等式
Rényi Entropy Power Inequalities via Normal Transport and Rotation
摘要：
在最近证明香农熵幂不等式（EPI）之后，提出了一个用于推导雷尼熵的各种EPI的综合框架，该框架使用正常密度的传输参数和旋转变量的变化。简单的参数给出恢复以前已知的Rényi EPIs和导出新的，通过统一的乘法形式与常数c和以前的作品与指数α的修改。特别是，对数凹密度，我们得到了一个简单的运输证明的一个尖锐的熵界。
英文摘要：
Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Rényi entropy is presented that uses transport arguments from normal densities and a change of variable by rotation. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound.
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