  Random correlation matrices are studied for both theoretical interestingness
and importance for applications. The author of [6] is interested in their
interpretation as covariance matrices of purely random signals, the authors of
[16] employ them in the generation of random clusters for studying clustering
methods, whereas the authors of [8] use them for studying subset selection in
multiple regression, etc. The determinant of a matrix is one of the most basic
and important matrix functions, and this makes studying the distribution of the
determinant of a random correlation matrix of paramount importance. Our main
result gives the asymptotic distribution of the determinant of a random
correlation matrix sampled from a uniform distribution over the space of $d
\times d$ 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, proven in [15], is investigated.

Probability