Moment-entropy inequalities

Research output: Contribution to journalArticle

Abstract

It is shown that the product of the Rényi entropies of two independent random vectors provides a sharp lower bound for the expected value of the moments of the inner product of the random vectors. This new inequality contains important geometry (such as extensions of one of the fundamental affine isoperimetric inequalities, the Blaschke-Santaló inequality).

Original languageEnglish (US)
Pages (from-to)757-774
Number of pages18
JournalAnnals of Probability
Volume32
Issue number1 B
DOIs
StatePublished - Jan 2004

Keywords

  • Blaschke-Santaló inequality
  • Dual mixed volumes
  • Rényi entropy

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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