  For the correlated Gaussian Wishart ensemble we compute the distribution of
the smallest eigenvalue and a related gap probability.We obtain exact results
for the complex (\beta=2) and for the real case (\beta=1). For a particular set
of empirical correlation matrices we find universality in the spectral density,
for both real and complex ensembles and all kinds of rectangularity. We
calculate the asymptotic and universal results for the gap probability and the
distribution of the smallest eigenvalue. We use the Supersymmetry method, in
particular the generalized Hubbard-Stratonovich transformation and
superbosonization.
