1997/05/06 by P. Zinn-Justin · 4 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Mathematical functions and polynomials #Random Matrices and Applications #cond-mat #hep-th
paper · pdf · doi:10.1007/s002200050372
published as Commun. Math. Phys. 194, 631-650 (1998) · 29 pages, TeX
arxiv created 1997/05/06 · openalex publication_date 1998/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.