Limiting spectral distribution of a new random matrix model with dependence across rows and columns

详细信息	查看全文 | 推荐本文 |

• 作者：Oliver Pfaffel ^{pfaffel@ma.tum.de} ; Eckhard Schlemm ; ^{schlemm@ma.tum.de}
• 关键词：Primary ; 15A52 ; Secondary ; 62M10
• 刊名：Linear Algebra and its Applications
• 出版年：2012
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：1 May, 2012
• 卷：436
• 期：9
• 页码：2966-2979
• 文件大小：334 K

摘要

We introduce a random matrix model where the entries are dependent across both rows and columns. More precisely, we investigate matrices of the form derived from a linear process , where the are independent random variables with bounded fourth moments. We show that, when both p and n tend to infinity such that the ratio converges to a finite positive limit y, the empirical spectral distribution of converges almost surely to a deterministic measure. This limiting measure, which depends on y and the spectral density of the linear process , is characterized by an integral equation for its Stieltjes transform. The matrix can be interpreted as an approximation to the sample covariance matrix of a high-dimensional process whose components are independent copies of .