A reverse entropy power inequality for i.i.d. log-concave random variables
Abstract
We show that h∞(X+Y)≤ h∞(Z+W), where X, Y are independent log-concave random variables, and Z, W are exponential random variables having the same respective ∞-R\'enyi entropies. Analogs for integer-valued monotone log-concave random variables are also obtained. Our main tools are decreasing rearrangement, majorization, and the change of measure.
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