Concentration of the information in data with log-concave distributions

Sergey Bobkov; Mokshay Madiman

doi:10.1214/10-AOP592

Concentration of the information in data with log-concave distributions

Sergey Bobkov, Mokshay Madiman

Mathematics

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56 Scopus citations

Abstract

A concentration property of the functional - log f(X) is demonstrated, when a random vector X has a log-concave density f on Rⁿ. This concentration property implies in particular an extension of the Shannon-McMillan-Breiman strong ergodic theorem to the class of discrete-time stochastic processes with log-concave marginals.

Original language	English (US)
Pages (from-to)	1528-1543
Number of pages	16
Journal	Annals of Probability
Volume	39
Issue number	4
DOIs	https://doi.org/10.1214/10-AOP592
State	Published - Jul 2011

Keywords

Asymptotic equipartition property
Concentration
Entropy
Log-concave distributions
Shannon-Mcmillan-Breiman theorem

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abstract = "A concentration property of the functional - log f(X) is demonstrated, when a random vector X has a log-concave density f on Rn. This concentration property implies in particular an extension of the Shannon-McMillan-Breiman strong ergodic theorem to the class of discrete-time stochastic processes with log-concave marginals.",

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KW - Shannon-Mcmillan-Breiman theorem

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Concentration of the information in data with log-concave distributions

Abstract

Keywords

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