The asymptotic distribution of the determinantrnof a random correlation matrix

摘要

Our main result gives the asymptotic distribution of the determinantrnof a random correlation matrix sampled in a particular way from thernspace of d×d correlation matrices. Several spin-off results are provenrnalong the way, and an interesting connection with the law of therndeterminant of general random matrices is investigated. As differentrnmethods for generating random correlation matrices are proposed inrnthe literature, one application of our result is that in can be employedrnto differentiate between those methods.