The Annals of Probability

Moment-entropy inequalities

Erwin Lutwak, Deane Yang, and Gaoyong Zhang

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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

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

First available in Project Euclid: 11 March 2004

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Zentralblatt MATH identifier

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

Blaschke--Santaló inequality Rényi entropy dual mixed volumes


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

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