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arXiv · 1012.5457

Concentration of the information in data with log-concave distributions

Sergey Bobkov·Mokshay Madiman
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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 $\mathbb{R}^n$. 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.

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Sergey Bobkov, Mokshay Madiman. 2010-12-25. Concentration of the information in data with log-concave distributions. https://doi.org/10.1214/10-aop592

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