科研之友
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摘要
We consider the number of eigenvalues which fall into an interval for the complex sample covariance matrices. The central limit theorem and a moderate deviation principle are established when the endpoint of the interval is close to the edge of the spectrum. The proofs depend on the Four Moment Theorem about the local statistics of eigenvalues up to edge, and the rigidity theorem of the eigenvalues for sample covariance matrices.
