Abstract:
We present a version of the 1/n-expansion for random matrix ensembles known as matrix models. The case where the support of the density of states of an ensemble consists of one interval and the case where the density of states is even and its support consists of two symmetric intervals is treated. In these cases we construct the expansion scheme for the Jacobi matrix determining a large class of expectations of symmetric functions of eigenvalues of random matrices, prove the asymptotic character of the scheme and give an explicit form of the first two terms. This allows us, in particular, to clarify certain theoretical physics results on the variance of the normalized traces of the resolvent of random matrices. We also find the asymptotic form of several related objects, such as smoothed squares of certain orthogonal polynomials, the normalized trace and the matrix elements of the resolvent of the Jacobi matrices, etc.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received: 9 November 2000 / Accepted: 26 July 2001
Rights and permissions
About this article
Cite this article
Albeverio, S., Pastur, L. & Shcherbina, M. On the 1/n Expansion for Some Unitary Invariant Ensembles of Random Matrices. Commun. Math. Phys. 224, 271–305 (2001). https://doi.org/10.1007/s002200100531
Published:
Issue Date:
DOI: https://doi.org/10.1007/s002200100531