Renyi Entropy Power Inequalities via Normal Transport and Rotation

Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Renyi 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 Renyi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent alpha of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound.