5 papers
Sampling Matrices from Harish-Chandra-Itzykson-Zuber Densities with Applications to Quantum Inference and Differential Privacy
Jonathan Leake, Colin S. McSwiggen, Nisheeth K. Vishnoi
Given two Hermitian matrices and , the Harish-Chandra-Itzykson-Zuber (HCIZ) distribution on the unitary group is , whe…
Majorization and Spherical Functions
Colin McSwiggen, Jonathan Novak
Majorization is a partial order on real vectors which plays an important role in a variety of subjects, ranging from algebra and combinatorics to probability and statistics. In thi…
Box splines, tensor product multiplicities and the volume function
Colin McSwiggen
We study the relationship between the tensor product multiplicities of a compact semisimple Lie algebra and a special function associated to $\mathfrak…
Revisiting Horn's Problem
Robert Coquereaux, Colin McSwiggen, Jean-Bernard Zuber
We review recent progress on Horn's problem, which asks for a description of the possible eigenspectra of the sum of two matrices with known eigenvalues. After revisiting the class…
On Horn's Problem and its Volume Function
Robert Coquereaux, Colin McSwiggen, Jean-Bernard Zuber
We consider an extended version of Horn's problem: given two orbits and of a linear representation of a compact Lie group, let ,…