A reverse entropy power inequality for i.i.d. log-concave random variables
Probability
2025-11-03 v2 Information Theory
Functional Analysis
math.IT
Metric Geometry
Abstract
We show that , where are independent log-concave random variables, and 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.
Cite
@article{arxiv.2510.09206,
title = {A reverse entropy power inequality for i.i.d. log-concave random variables},
author = {Zhen Fu and Jiange Li},
journal= {arXiv preprint arXiv:2510.09206},
year = {2025}
}