Exact Density of States for finite Gaussian Random Matrix Ensembles via Supersymmetry
Frieder Kalisch, Daniel Braak
Abstract
We calculate the exact density of states (DOS) for the three classical and two non-classical Random Matrix Ensembles for finite matrix size N using supersymmetric integrals. The 1/N-Expansion yields already in lowest order good approximations to the exact result even for small values of N~5. We conjecture a connection between the N-dependence of the oscillating part of the DOS and the short-distance behavior of the two-level correlation function.
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