THE LARGEST SAMPLE EIGENVALUE DISTRIBUTION IN THE RANK 1 QUATERNIONIC SPIKED MODEL OF WISHART ENSEMBLE

被引：15
|
作者：
Wang, Dong [1 ]
机构：
[1] Brandeis Univ, Dept Math, Waltham, MA 02454 USA
来源：
ANNALS OF PROBABILITY | 2009年 / 37卷 / 04期
关键词：
Wishart distribution; quaternionic spiked model; SPACING DISTRIBUTIONS; ORTHOGONAL POLYNOMIALS; ASYMPTOTICS; EDGE; HARD;
D O I：
10.1214/08-AOP432
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We solve the largest sample eigenvalue distribution problem in the rank I spiked model of the quaternionic Wishart ensemble, which is the first case of a statistical generalization of the Laguerre symplectic ensemble (LSE) on the soft edge. We observe a phase change phenomenon similar to that in the complex case, and prove that the new distribution at the phase change point is the GOE Tracy-Widom distribution.
引用
收藏
页码：1273 / 1328
页数：56
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