Density of states for GUE, GOE, and interpolating ensembles through supersymmetric approach

Abstract

We use the supersymmetric formalism to derive an integral formula for the density of states of the Gaussian Orthogonal Ensemble, and then apply saddle-point analysis to give a new derivation of the 1/N-correction to Wigner's law. This extends the work of Disertori on the Gaussian Unitary Ensemble. We also apply our method to the interpolating ensembles of Mehta--Pandey.

22 pp. Added interpolating ensembles of Mehta--Pandey. To appear in J. Math. Phys. Fixed 2 typos

References in corpus (1)

• On the second mixed moment of the characteristic polynomials of the 1D band matrices

Cited by in corpus (1)

• The Wilson loop in the Gaussian Unitary Ensemble