← 研踪 PaperTrailarXiv:2510.09206 · v4
A reverse entropy power inequality for i.i.d. log-concave random variables
首次提交 2025-10-10 17:44
版本更新 2026-11-09 14:06
雷达观测 2026-11-10 13:18
摘要
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.
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v4 · 2026-11-09 14:06 · 最新观测版本
A reverse entropy power inequality for i.i.d. log-concave random variables
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.
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