Concentration of the information in data with log-concave distributions

Sergey Bobkov, Mokshay Madiman

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1528-1543
Number of pages16
JournalAnnals of Probability
Volume39
Issue number4
DOIs
StatePublished - Jul 2011

Keywords

  • Asymptotic equipartition property
  • Concentration
  • Entropy
  • Log-concave distributions
  • Shannon-Mcmillan-Breiman theorem

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