Gaussian Width of Convex Sets via Integral Decompositions, Projections, and the Distribution of Intrinsic Volumes

Reese Pathak, Nikita Zhivotovskiy

We revisit the problem of bounding the expected supremum of a canonical Gaussian process indexed by a convex set $T\subset {\mathbf{R}}^d$. We develop two decompositions for the Gau…