Density of States for Gue Through Supersymmetric Approach

The supersymmetric approach has proved to be a powerful tool for the study of random systems where classical techniques do not seem to apply. It also seems promising for rigorous analysis. In this context, we consider the GUE density of states, and show that, using the supersymmetric approach, we can rigorously re-derive the results obtained by classical techniques (orthogonal polynomials), in all energy regions (inside the spectrum, at the edge and outside the spectrum).