The Wilson loop in the Gaussian Unitary Ensemble

Abstract

Using the supersymmetric formalism we compute exactly at finite $N$ the expectation of the Wilson loop in the Gaussian Unitary Ensemble and derive an exact formula for the spectral density at finite $N$. We obtain the same result by a second method relying on enumerative combinatorics and show that it leads to a novel proof of the Harer-Zagier series formula.

references added, misprints corrected

References in corpus (3)

• A simple model of trees for unicellular maps
• Random Matrices and the Anderson Model
• Density of states for GUE, GOE, and interpolating ensembles through supersymmetric approach

Cited by in corpus (1)

• Wigner law for matrices with dependent entries - a perturbative approach