English

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 h(X+Y)h(Z+W)h_\infty(X+Y)\leq h_\infty(Z+W), where X,YX, Y are independent log-concave random variables, and Z,WZ, W are exponential random variables having the same respective \infty-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}
}
R2 v1 2026-07-01T06:29:04.030Z