Sharp Rogers--Shephard Inequalities for Rényi Entropy

Bang-Xian Han, Guoqing Zhan, Chiyu Zhou +1

We establish sharp weighted Rogers--Shephard inequalities for Rényi differential entropy. For independent copies $X,X^{\prime }$ of a log-concave random vector in ${\mathbb{R}}^n$, we prove $h_p(aX-b…