The Annals of Probability

Moment-entropy inequalities

Erwin Lutwak, Deane Yang, and Gaoyong Zhang

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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).

Article information

Source
Ann. Probab. Volume 32, Number 1B (2004), 757-774.

Dates
First available in Project Euclid: 11 March 2004

Permanent link to this document
http://projecteuclid.org/euclid.aop/1079021463

Digital Object Identifier
doi:10.1214/aop/1079021463

Mathematical Reviews number (MathSciNet)
MR2039942

Zentralblatt MATH identifier
02100733

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 94A17: Measures of information, entropy 52A40: Inequalities and extremum problems

Keywords
Blaschke--Santaló inequality Rényi entropy dual mixed volumes

Citation

Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong. Moment-entropy inequalities. Ann. Probab. 32 (2004), no. 1B, 757--774. doi:10.1214/aop/1079021463. http://projecteuclid.org/euclid.aop/1079021463.


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