Intrinsic volumes and Gaussian polytopes: the missing piece of the jigsaw

TL;DR

This paper establishes a lower variance bound for intrinsic volumes of Gaussian polytopes, demonstrating that normalized variances converge to positive limits, thus filling a crucial gap in the understanding of Gaussian polytope theory.

Contribution

It provides the first lower variance bound for intrinsic volumes of Gaussian polytopes and discusses its implications in the broader theory.

Findings

Variance bounds are established for intrinsic volumes.

Normalized variances converge to positive limits.

Fills a key gap in Gaussian polytope theory.

Abstract

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.