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	Fixed trace beta-Hermite ensembles: Asymptotic eigenvalue density and the edge of the density
	Zhou, Da-Sheng ; Liu, Dang-Zheng ; Qian, Tao
	2010
关键词	eigenvalues and eigenfunctions matrix algebra RANDOM-MATRIX ENSEMBLES SUPERSYMMETRY DISTRIBUTIONS DETERMINANT
英文摘要	In the present paper, fixed trace beta-Hermite ensembles generalizing the fixed trace Gaussian ensembles are considered. For all beta, we prove the Wigner semicircle law for these ensembles by using two different methods: one is the moment equivalence method with the help of the matrix model for general beta, the other is to use asymptotic analysis tools. At the edge of the density, we prove that the edge scaling limit for beta-HE implies the same limit for fixed trace beta-Hermite ensembles. Consequently, explicit limit can be given for fixed trace Gaussian orthogonal, unitary, and symplectic ensembles. Furthermore, for even beta, analogous to beta-Hermite ensembles, a multiple integral of the Konstevich type can be obtained.; Physics, Mathematical; SCI(E); 3; ARTICLE; 3; 51
语种	英语
出处	SCI
出版者	数学物理杂志
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/244685]
专题	数学科学学院
推荐引用方式 GB/T 7714	Zhou, Da-Sheng,Liu, Dang-Zheng,Qian, Tao. Fixed trace beta-Hermite ensembles: Asymptotic eigenvalue density and the edge of the density. 2010-01-01.

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