Moment-entropy inequalities

Erwin Lutwak, Deane Yang, Gaoyong Zhang

Research output: Contribution to journalArticlepeer-review


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
Issue number1 B
StatePublished - Jan 2004


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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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