Random matrices and the replica method

Recently, a discussion was revived about applicability of the replica approach to description of spectral fluctuations in the context of random matrix theory and beyond. The present paper, concentrating on invariant non-gaussian random matrix ensembles with orthogonal, unitary and symplectic symmetries, aims to demonstrate that both the bosonic and the fermionic replicas are capable of reproducing nonperturbative fluctuation formulas for spectral correlation functions in entire energy scale, including the self-correlation of energy levels. The framework proposed does not rely on traditional σ-model mapping.