文摘
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 .