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.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- 1998
- DOI:
- 10.1007/s002200050372
- arXiv:
- arXiv:cond-mat/9705044
- Bibcode:
- 1998CMaPh.194..631Z
- Keywords:
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- Condensed Matter;
- High Energy Physics - Theory
- E-Print:
- 29 pages, TeX