On the concentration of random multilinear forms and the universality of random block matrices

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• 作者：Hoi H. Nguyen ; Sean O’Rourke
• 关键词：15A52 ; 15A63 ; 11B25
• 刊名：Probability Theory and Related Fields
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：162
• 期：1-2
• 页码：97-154
• 全文大小：1,260 KB
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• 作者单位：Hoi H. Nguyen (1)
  Sean O’Rourke (2)
  
  1. Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA
  2. Department of Mathematics, Yale University, New Haven, CT, 06520, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Probability Theory and Stochastic Processes
  Mathematical and Computational Physics
  Quantitative Finance
  Mathematical Biology
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Operation Research and Decision Theory
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-2064

文摘

The circular law asserts that if \({\mathbf {X}}_n\) is a \(n \times n\) matrix with iid complex entries of mean zero and unit variance, then the empirical spectral distribution of \(\frac{1}{\sqrt{n}} {\mathbf {X}}_n\) converges almost surely to the uniform distribution on the unit disk as \(n\) tends to infinity. Answering a question of Tao, we prove the circular law for a general class of random block matrices with dependent entries. The proof relies on an inverse-type result for the concentration of linear operators and multilinear forms.