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.