The spectrum edge of random matrix ensembles

The scaled n-level distribution and scaled level spacing distribution for the small and large eigenvalues of various ensembles of random matrices are considered. Exact results for both these quantities are obtained for various special values of the parameters in the gaussian and Laguerre ensembles....

Full description

Saved in:
Bibliographic Details
Published in:Nuclear physics. B 1993-08, Vol.402 (3), p.709-728
Main Author: Forrester, P.J.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Logic, set theory, and algebra
Mathematical methods in physics
Physics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The scaled n-level distribution and scaled level spacing distribution for the small and large eigenvalues of various ensembles of random matrices are considered. Exact results for both these quantities are obtained for various special values of the parameters in the gaussian and Laguerre ensembles. On the basis of a Coulomb gas analogy, an asymptotic formula for the distribution of the smallest and largest eigenvalue is given in terms of the eigenvalue density at the spectrum edge.
ISSN:0550-3213
1873-1562
DOI:10.1016/0550-3213(93)90126-A