Intrinsic Volumes and Gaussian Polytopes: The Missing Piece of the Jigsaw

The intrinsic volumes of Gaussian polytopes are considered. A lower variance bound for these quantities is proved, showing that, under suitable normalization, the variances converge to strictly positive limits. The implications of this missing piece of the jigsaw in the theory of Gaussian polytopes are discussed.

2010 Mathematics Subject Classification: Primary 60D05; Secondary 52A22.

Keywords and Phrases: Gaussian polytopes, random polytopes, stochastic geometry, variance lower bound.

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