Mourtada

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

arXiv:2603.02714v2 Announce Type: replace-cross Abstract: 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 Gaussian width, based on the geometry of the index set. The first decomposition involves metric projections of Gaussians onto rescaled copies of $T$. The second involves fixed points arising from a quadratically penalized variant of the local width. Neither...