Universality of correlation functions of Hermitian random matrices in an external field

Abstract

The behavior of correlation functions is studied in a class of matrix models characterized by a measure exp(-S) containing a potential term and an external source term: S = N tr(V(M) - MA). In the large N limit, the short-distance behavior is found to be identical to the one obtained in previously studied matrix models, thus extending the universality of the level-spacing distribution. The calculation of correlation functions involves (finite N) determinant formulae, reducing the problem to the large N asymptotic analysis of a single kernel K. This is performed by an appropriate matrix integral formulation of K. Multi-matrix generalizations of these results are discussed.