The Annals of Probability

Concentration of the information in data with log-concave distributions

Sergey Bobkov and Mokshay Madiman

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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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Ann. Probab., Volume 39, Number 4 (2011), 1528-1543.

First available in Project Euclid: 5 August 2011

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Zentralblatt MATH identifier

Primary: 60G07: General theory of processes 94A15: Information theory, general [See also 62B10, 81P94]

Concentration entropy log-concave distributions asymptotic equipartition property Shannon–McMillan–Breiman theorem


Bobkov, Sergey; Madiman, Mokshay. Concentration of the information in data with log-concave distributions. Ann. Probab. 39 (2011), no. 4, 1528--1543. doi:10.1214/10-AOP592.

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