A min-entropy power inequality for groups

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 power inequality is conjectured and a partial result proved.

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