Maxima of entries of Haar distributed matrices

• 成果类型: Article
• 署名作者: Jiang, TF
• 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/s00440-004-0376-5
• 发表日期: 2005
• 页码: 121-144
• 关键词: eigenvalues

摘要

Let Gamma(n)=(gamma(ij)) be an nxn random matrix such that its distribution is the normalized Haar measure on the orthogonal group O(n). Let also W-n:=max(1less than or equal toi,jless than or equal ton)|gamma(ij)|. We obtain the limiting distribution and a strong limit theorem on W-n. A tool has been developed to prove these results. It says that up to n/(log n)(2) columns of Gamma(n) can be approximated simultaneously by those of some Y-n=(y(ij)) in which y(ij) are independent standard normals. Similar results are derived also for the unitary group U(n), the special orthogonal group SO(n), and the special unitary group SU(n).