Entropy-variance inequalities for discrete log-concave random variables via degree of freedom
Probability
2023-09-08 v4 Information Theory
math.IT
Abstract
We utilize a discrete version of the notion of degree of freedom to prove a sharp min-entropy-variance inequality for integer valued log-concave random variables. More specifically, we show that the geometric distribution minimizes the min-entropy within the class of log-concave probability sequences with fixed variance. As an application, we obtain a discrete R\'enyi entropy power inequality in the log-concave case, which improves a result of Bobkov, Marsiglietti and Melbourne (2022).
Keywords
Cite
@article{arxiv.2212.09115,
title = {Entropy-variance inequalities for discrete log-concave random variables via degree of freedom},
author = {Heshan Aravinda},
journal= {arXiv preprint arXiv:2212.09115},
year = {2023}
}
Comments
The final version uploaded; To appear in Discrete Mathematics