Approximation of Haar distributed matrices and limiting distributions of eigenvalues of Jacobi ensembles

• 成果类型: Article
• 署名作者: Jiang, Tiefeng
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-008-0146-x
• 发表日期: 2009
• 页码: 221-246
• 关键词: smallest eigenvalue; spectral-analysis; roots; THEOREMS; ENTRIES; models; bounds

摘要

We develop a tool to approximate the entries of a large dimensional complex Jacobi ensemble with independent complex Gaussian random variables. Based on this and the author's earlier work in this direction, we obtain the Tracy-Widom law of the largest singular values of the Jacobi emsemble. Moreover, the circular law, the Marchenko-Pastur law, the central limit theorem, and the laws of large numbers for the spectral norms are also obtained.