2011/07/07 by Romain Couillet, Couillet, Romain, Walid Hachem +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Blind Source Separation Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #Quantum Information and Cryptography #Quantum optics and atomic interactions #Random Matrices and Applications #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1107.1409
To appear in IEEE Transactions on Information Theory, 2012
openalex publication_date 2011/07/07 · arxiv created 2012/06/19 · arxiv updated 2012/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, 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 (GUE). 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.