The Largest Eigenvalue of Real Symmetric,Hermitian and Hermitian Self-dual Random Matrix Models with Rank One External Source,Part I |
| |
Authors: | Dong Wang |
| |
Institution: | 1.Department of Mathematics,University of Michigan,Ann Arbor,USA |
| |
Abstract: | We consider the limiting location and limiting distribution of the largest eigenvalue in real symmetric (β=1), Hermitian (β=2), and Hermitian self-dual (β=4) random matrix models with rank 1 external source. They are analyzed in a uniform way by a contour integral representation
of the joint probability density function of eigenvalues. Assuming the “one-band” condition and certain regularities of the
potential function, we obtain the limiting location of the largest eigenvalue when the nonzero eigenvalue of the external
source matrix is not the critical value, and further obtain the limiting distribution of the largest eigenvalue when the nonzero
eigenvalue of the external source matrix is greater than the critical value. When the nonzero eigenvalue of the external source
matrix is less than or equal to the critical value, the limiting distribution of the largest eigenvalue will be analyzed in
a subsequent paper. In this paper we also give a definition of the external source model for all β>0. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|