## 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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### References:

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