Universality results for the largest eigenvalues of some sample covariance matrix ensembles

• 成果类型: Article
• 署名作者: Peche, Sandrine
• 署名单位: Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-007-0133-7
• 发表日期: 2009
• 页码: 481-516
• 关键词: limit; edge; distributions; spectrum; complex

摘要

For sample covariance matrices with i.i.d. entries with sub-Gaussian tails, when both the number of samples and the number of variables become large and the ratio approaches one, it is a well-known result of Soshnikov that the limiting distribution of the largest eigenvalue is same that of Gaussian samples. In this paper, we extend this result to two cases. The first case is when the ratio approaches an arbitrary finite value. The second case is when the ratio becomes infinite or arbitrarily small.