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Sharp phase transitions in Euclidean integral geometry
Martin Lotz, Joel A. Tropp
The intrinsic volumes of a convex body are fundamental invariants that capture information about the average volume of the projection of the convex body onto a random subspace of f…
Concentration of the Intrinsic Volumes of a Convex Body
Martin Lotz, Michael B. McCoy, Ivan Nourdin +2
The intrinsic volumes are measures of the content of a convex body. This paper uses probabilistic and information-theoretic methods to study the sequence of intrinsic volumes of a…
Simplicial faces of the set of correlation matrices
Joel A. Tropp
This paper concerns the facial geometry of the set of correlation matrices. The main result states that almost every set of vertices generates a simplicial face, p…
Integer factorization of a positive-definite matrix
Joel A. Tropp
This paper establishes that every positive-definite matrix can be written as a positive linear combination of outer products of integer-valued vectors whose entries are bounded by…
From Steiner Formulas for Cones to Concentration of Intrinsic Volumes
Michael B. McCoy, Joel A. Tropp
The intrinsic volumes of a convex cone are geometric functionals that return basic structural information about the cone. Recent research has demonstrated that conic intrinsic volu…
Constructing packings in Grassmannian manifolds via alternating projection
I. S. Dhillon, R. W. Heath, T. Strohmer +1
This paper describes a numerical method for finding good packings in Grassmannian manifolds equipped with various metrics. This investigation also encompasses packing in projective…