Concentration of the information in data with log-concave distributions

Sergey Bobkov; Mokshay Madiman

doi:10.1214/10-AOP592

Concentration of the information in data with log-concave distributions

Probability 2012-11-20 v2 Functional Analysis

Authors: 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.

Keywords

limit theorems probability distribution ergodic theory

Cite

@article{arxiv.1012.5457,
  title  = {Concentration of the information in data with log-concave distributions},
  author = {Sergey Bobkov and Mokshay Madiman},
  journal= {arXiv preprint arXiv:1012.5457},
  year   = {2012}
}

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Published in at http://dx.doi.org/10.1214/10-AOP592 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Concentration of the information in data with log-concave distributions

Abstract

Keywords

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