Matrix form of the Brunn-Minkowski inequality

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Abstract

The well-known Brunn-Minkowski Inequality (BMI) is one of the basic inequalities in geometry. A formal statement of this inequality is presented. The BMI is dual in some sense to the Entropy-Power Inequality (EPI), which lower bounds the entropy-power of the sum of independent random variables. A matrix form for the EPI has been derived previously, and some of its applications have been pointed out. Analogously, a matrix form for the BMI is derived, and its applications discussed.

Original languageEnglish
Pages71
Number of pages1
StatePublished - 1995
Externally publishedYes
EventProceedings of the 1995 IEEE International Symposium on Information Theory - Whistler, BC, Can
Duration: 17 Sep 199522 Sep 1995

Conference

ConferenceProceedings of the 1995 IEEE International Symposium on Information Theory
CityWhistler, BC, Can
Period17/09/9522/09/95

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