Random Hermitian matrices in an external field

Abstract

In this article, a model of random Hermitian matrices is considered, in which the measure exp(-S) contains a general U(N)-invariant potential and an external source term: S = N tr(V(M) + MA). The generalization of known determinant formulae leads to compact expressions for the correlation functions of the energy levels. These expressions, exact at finite N, are potentially useful for asymptotic analysis. © 1997 Elsevier Science B.V.