Local Failure Detection and Diagnosis in Large Sensor Networks

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In this paper, the joint fluctuations of the extreme eigenvalues and eigenvectors of a large dimensional sample covariance matrix are analyzed when the associated population covariance matrix is a finite-rank perturbation of the identity matrix, which corresponds to a so-called spiked model in random matrix theory. The asymptotic fluctuations, as the matrix size grows large, are shown to be intimately linked with matrices from the Gaussian Unitary Ensemble (GUE). When the spiked population eigenvalues have unit multiplicity, the fluctuations follow a central limit theorem.