Replica Method for Wide Correlators in Gaussian Orthogonal, Unitary And Symplectic Random Matrix Ensembles

Abstract

We calculate connected correlators in Gaussian orthogonal, unitary and symplectic random matrix ensembles by the replica method in the 1/N-expansion. We obtain averaged one-point Green's functions up to the next-to-leading order O(1/N) and wide two-level correlators up to the first nontrivial order O(1/N^2) and wide three-level correlators up to the first nontrivial order $O(1/N^4)$ by carefully treating fluctuations in saddle-point evaluation.

LaTeX 21 pages, a new result on wide three-level correlators added

References in corpus (5)

• Higher genus correlators for the hermitian matrix model with multiple cuts
• Correlations of Nearby Levels Induced by a Random Potential
• New universal spectral correlators
• Universal Wide Correlators in Non-Gaussian Orthogonal, Unitary and Symplectic Random Matrix Ensembles
• Diagrammatic Method for Wide Correlators in Gaussian Orthogonal and Symplectic Random Matrix Ensembles

Cited by in corpus (4)

• Wigner-Dyson Statistics from the Replica Method
• Exact Density of States for finite Gaussian Random Matrix Ensembles via Supersymmetry
• Universal Wide Correlators in Non-Gaussian Orthogonal, Unitary and Symplectic Random Matrix Ensembles
• Replica-symmetric approach to the typical eigenvalue fluctuations of Gaussian random matrices