A class of multivariate polynomial convolutions (and applications)

Abstract

We prove two "master" convolution theorems for multivariate determinantal polynomials. The methods used include basic properties of what we call a "minor-orthogonal" ensemble as well as properties of the mixed discriminant of matrices. We also give applications, including a rederivation of a result of Barvinok on computing the permanent of a low rank matrix and a polynomial convolution corresponding to the unitarily invariant addition of generalized singular values.