Minimum entropy of a log-concave variable for fixed variance

2023/09/04 by Melbourne, James, Nayar, Piotr, Roberto, Cyril · 2 citations
#FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Probability (math.PR)

paper · doi:10.48550/arxiv.2309.01840

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.

Cited by

• Entropic analogues of Grünbaum's inequality
• A Quantitative Entropy Power Inequality for Dependent Random Vectors

Related

• A reverse entropy power inequality for i.i.d. log-concave random variables
• Rényi entropy and variance comparison for symmetric log-concave random variables
• Log-concavity and discrete degrees of freedom
• Concentration functions and entropy bounds for discrete log-concave distributions
• A strengthened entropy power inequality for log-concave densities