A reverse entropy power inequality for i.i.d. log-concave random variables

2025/10/10 by Zhen Fu, Jiange Li, Fu, Zhen +1
#math.PR #cs.IT #math.FA #math.IT #math.MG

paper · pdf · doi:10.48550/arxiv.2510.09206

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 ∞-Rényi 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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