Minimum entropy of a log-concave variable for fixed variance

Autor:	Melbourne, James, Nayar, Piotr, Roberto, Cyril
Rok vydání:	2023
Předmět:	Mathematics - Probability Computer Science - Information Theory
Druh dokumentu:	Working Paper
Popis:	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. Comment: A simpler proof of the "Three-point inequality'' is given
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.01840 Zobrazit plný text záznamu View this record from Arxiv