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Concentration of the information in data with log-concave distributions. (English) Zbl 1227.60043

Summary: A concentration property of the functional \(-\log f(X)\) is demonstrated for a random vector \(X\) that has a log-concave density \(f\) on \(\mathbb R^{n}\). 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.

MSC:

60G07 General theory of stochastic processes
94A15 Information theory (general)
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