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The joint fluctuations of the extreme eigen-values and eigenvectors of large sample covariance matrices of the spiked-model type are analyzed. This result is used to develop an original framework for the diagnosis of local failures in sensor networks, corroborated by simulations. One of the elementary requests for fault diagnosis is the fast, reliable and computationally light identification of a system failure. In dynamical scenarios, those systems are made of fluctuating parameters whose evolutions are tracked by a noisy sensor measures, which become increasingly difficult to fast process in recent large networks.
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