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
StatePublished - Jan 2004

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Moment Inequalities
Entropy Inequality
Random Vector
Isoperimetric Inequality
Expected Value
Scalar, inner or dot product
Entropy
Lower bound
Moment

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Moment-entropy inequalities. / Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong.

In: Annals of Probability, Vol. 32, No. 1 B, 01.2004, p. 757-774.

Research output: Contribution to journalArticle

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