Variants of the Entropy Power Inequality

Abstract

An extension of the entropy power inequality to the form $N_r^{\alpha }(X+Y)\ge N_r^{\alpha }(X)+N_r^{\alpha }(Y)$ with arbitrary independent summands $X$ and $Y$ in ${\mathbb{R}}^n$ is obtained for the Rényi entropy and powers $\alpha \ge (r+1)/2$.

6 pages, two-column format