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

Дата и время публикации : 1997-05-06T14:02:21Z

Авторы публикации и институты :
P. Zinn-Justin

Ссылка на журнал-издание: Commun. Math. Phys. 194, 631-650 (1998)
Коментарии к cтатье: 29 pages, TeX
Первичная категория: cond-mat

Все категории : cond-mat, hep-th

Краткий обзор статьи: 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: $S=Ntr(V(M)-MA)$. 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.

Category: Physics