Minimum entropy of a log-concave variable for fixed variance
Probability
2024-03-19 v2 Information Theory
math.IT
Abstract
We show that for log-concave real random variables with fixed variance the Shannon differential entropy is minimized for an exponential random variable. We apply this result to derive upper bounds on capacities of additive noise channels with log-concave noise. We also improve constants in the reverse entropy power inequalities for log-concave random variables.
Cite
@article{arxiv.2309.01840,
title = {Minimum entropy of a log-concave variable for fixed variance},
author = {James Melbourne and Piotr Nayar and Cyril Roberto},
journal= {arXiv preprint arXiv:2309.01840},
year = {2024}
}
Comments
A simpler proof of the "Three-point inequality'' is given