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Moment-Entropy Inequalities

Erwin Lutwak, Deane Yang and Gaoyong Zhang
The Annals of Probability
Vol. 32, No. 1, B (Jan., 2004), pp. 757-774
Stable URL: http://www.jstor.org/stable/3481617
Page Count: 18
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Moment-Entropy Inequalities
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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).

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