Random Hermitian matrices in an external field Original Research Article

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 = Ntr(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.