Replica method for wide correlators in Gaussian orthogonal, unitary and symplectic random matrix ensembles

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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.