The asymptotic distribution of the determinant of a random correlation matrix

Abstract

Our main result gives the asymptotic distribution of the determinant of a random correlation matrix sampled in a particular way from the space of d×d correlation matrices. Several spin-off results are proven along the way, and an interesting connection with the law of the determinant of general random matrices is investigated. As different methods for generating random correlation matrices are proposed in the literature, one application of our result is that in can be employed to differentiate between those methods.