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We develop a general notion of rearrangement for certain metric groups, and prove a Hardy-Littlewood type inequality. Combining this with a characterization of the extreme points of the set of probability measures with bounded densities with respect to a reference measure, we establish a general min-entropy inequality for convolutions. Special attention is paid to the integers where a min-entropy...
An optimal ∞-Rényi entropy power inequality is derived for d-dimensional random vectors. In fact, the authors establish a matrix ∞-EPI analogous to the generalization of the classical EPI established by Zamir and Feder. The result is achieved by demonstrating uniform distributions as extremizers of a certain class of ∞-Rényi entropy inequalities, and then putting forth a new rearrangement inequality...
We explore conditions under which a reverse Rényi entropy power inequality holds for random vectors with s-concave densities, and also discuss connections with Convex Geometry.
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