  We study a new ensemble of random correlation matrices related to
multivariate Student (or more generally elliptic) random variables. We
establish the exact density of states of empirical correlation matrices that
generalizes the Marcenko-Pastur result. The comparison between the theoretical
density of states in the Student case and empirical financial data is
surprisingly good, even if we are still able to detect systematic deviations.
Finally, we compute explicitely the Kullback-Leibler entropies of empirical
Student matrices, which are found to be independent of the true correlation
matrix, as in the Gaussian case. We provide numerically exact values for these
Kullback-Leibler entropies.
