Abstract:We show that $h_\infty(X+Y)\leq h_\infty(Z+W)$, where $X, Y$ are independent log-concave random variables, and $Z, W$ are exponential random variables having the same respective $\infty$-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.
From: Jiange Li [view email]
[v1]
Fri, 10 Oct 2025 09:44:12 UTC (13 KB)
[v2]
Mon, 27 Oct 2025 10:43:04 UTC (13 KB)
[v3]
Tue, 21 Jul 2026 06:19:50 UTC (16 KB)
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