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摘要
We consider a class of matrices of the form C-n = (1/N)(Rn + sigma X-n)(R-n + sigma X-n)*, where Xn is an n x N matrix consisting of independent standardized complex entries, R-n is an n x N nonrandom matrix, and sigma > 0. Among several applications, C-n can be viewed as a sample correlation matrix, where information is contained in (1/N)RnRn*, but each column of R-n is contaminated by noise. As n ->infinity, if n/N -> c > 0, and the empirical distribution of the eigenvalues of (1/N)RnRn* converge to a proper probability distribution, then the empirical distribution of the eigenvalues of C-n converges a.s. to a nonrandom limit. In this paper we show that, under certain conditions on R-n, for any closed interval in R+ outside the support of the limiting distribution, then, almost surely, no eigenvalues of C-n will appear in this interval for all n large.
- 出版日期2012-1
- 单位东北师范大学
