Random matrices ensembles and the extensivity of the Sq entropy

We consider the joint density distribution of the elements of certain random matrix models which are example of globally correlated and asymptotically scale-invariant distributions. It is shown that in their cases, the nonadditive entropy $S_q$ is extensive only when the limit $q\rightarrow 1$ is taken. On the other hand, when restriction in the occupation of the phase space is imposed extensiveness is obtained for values of the entropic parameter different of one.