Abstract. The replica method has previously been used to calculate the semicircular averaged eigenvalue spectrum of the Gaussian orthogonal ensemble of real symmetric N*N random matrices in the limit where N to infinity . The authors develop a perturbative scheme which, within this same replica framework, is used to calculate the corrections within this semicircular band of eigenvalues to order 1/N and 1/N². A new and straightforward self-consistency argument is presented and used to derive the shape of the averaged eigenvalue spectrum when N is large but finite and the scaling behaviour of this averaged eigenvalue spectrum near the band edges is demonstrated in a straightforward fashion. Some comments are made on the relation of the results to those of field theoretical calculations in zero dimensions.

Print publication: Issue 23 (7 December 1990)