Work

Minimum entropy of a log-concave variable for fixed variance

Year: 2023

Type: preprint

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.

Source: HAL (Le Centre pour la Communication Scientifique Directe)

DOI: 10.48550/arxiv.2309.01840

Authors: Melbourne, James, Nayar, Piotr, Roberto, Cyril

Institutions: Mathematics Research Center, Centre National de la Recherche Scientifique, Université Paris Nanterre, Mathématiques Appliquées à Paris 5, Modélisation aléatoire de Paris Nanterre, Université Paris Descartes

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Narodowym Centrum Nauki, Centre National de la Recherche Scientifique, Institut Henri Poincaré

Awards: G3749866555, G8640654250, G872215882

OpenAlex ID: W4386557243

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