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

Details Universality of correlation functions of hermitian random matrices in an external field Universality of correlation functions of hermitian random matrices in an external field

1997-05-06

arxiv.org/abs/cond-mat/9705044v1

Commun. Math. Phys. 194, 631-650 (1998)

Physics

Condensed Matter

29 pages, TeX

Scientific paper

10.1007/s002200050372

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.

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