  We give a constructive proof for the superbosonization formula for invariant
random matrix ensembles, which is the supersymmetry analog of the theory of
Wishart matrices. Formulas are given for unitary, orthogonal and symplectic
symmetry, but worked out explicitly only for the orthogonal case. The method
promises to become a powerful tool for investigating the universality of
spectral correlation functions for a broad class of random matrix ensembles of
non-Gaussian type.
