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 , wide two-level correlators up to the first non-trivial order and wide three-level correlators up to the first non-trivial order by carefully treating fluctuations in saddle-point evaluation.