Random matrices and the replica method

Recently, a discussion was revived about applicability of the replica appro ach to description of spectral fluctuations in the context of random matrix theory and beyond. The present paper, concentrating on invariant non-gauss ian random matrix ensembles with orthogonal, unitary and symplectic symmetr ies, aims to demonstrate that both the bosonic and the fermionic replicas a re capable of reproducing nonperturbative fluctuation formulas for spectral correlation functions in entire energy scale, including the self-correlati on of energy levels. The framework proposed does not rely on traditional si gma -model mapping. (C) 2001 Elsevier Science B.V. All rights reserved.