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Journal Articles IEEE Transactions on Information Theory Year : 2013

Fluctuations of spiked random matrix models and failure diagnosis in sensor networks

Abstract

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, corresponding to the 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. When the spiked population eigenvalues have unit multiplicity, the fluctuations follow a central limit theorem. This result is used to develop an original framework for the detection and diagnosis of local failures in large sensor networks, for known or unknown failure magnitude.

Dates and versions

hal-00830228 , version 1 (04-06-2013)

Identifiers

Cite

Romain Couillet, Walid Hachem. Fluctuations of spiked random matrix models and failure diagnosis in sensor networks. IEEE Transactions on Information Theory, 2013, 59 (1), pp.509-525. ⟨10.1109/TIT.2012.2218572⟩. ⟨hal-00830228⟩
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