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July 2011 Concentration of the information in data with log-concave distributions
Sergey Bobkov, Mokshay Madiman
Ann. Probab. 39(4): 1528-1543 (July 2011). DOI: 10.1214/10-AOP592

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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Sergey Bobkov. Mokshay Madiman. "Concentration of the information in data with log-concave distributions." Ann. Probab. 39 (4) 1528 - 1543, July 2011. https://doi.org/10.1214/10-AOP592

Information

Published: July 2011
First available in Project Euclid: 5 August 2011

zbMATH: 1227.60043
MathSciNet: MR2857249
Digital Object Identifier: 10.1214/10-AOP592

Subjects:
Primary: 60G07 , 94A15

Keywords: asymptotic equipartition property , Concentration , Entropy , log-concave distributions , Shannon–McMillan–Breiman theorem

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 4 • July 2011
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