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

• 成果类型: Article
• 署名作者: Wang, Dong
• 署名单位: Brandeis University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP432
• 发表日期: 2009
• 页码: 1273-1328
• 关键词: spacing distributions; Orthogonal polynomials; asymptotics; edge; hard

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.