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.

29 pages, TeX

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