Moment-entropy inequalities

Erwin Lutwak; Deane Yang; Gaoyong Zhang

doi:10.1214/aop/1079021463

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Home > Journals > Ann. Probab. > Volume 32 > Issue 1B > Article

January 2004 Moment-entropy inequalities

Erwin Lutwak, Deane Yang, Gaoyong Zhang

Ann. Probab. 32(1B): 757-774 (January 2004). DOI: 10.1214/aop/1079021463

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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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Erwin Lutwak. Deane Yang. Gaoyong Zhang. "Moment-entropy inequalities." Ann. Probab. 32 (1B) 757 - 774, January 2004. https://doi.org/10.1214/aop/1079021463