Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
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Publication:2571691
DOI10.1214/009117905000000233zbMATH Open1086.15022arXivmath/0403022OpenAlexW2066459155WikidataQ56813022 ScholiaQ56813022MaRDI QIDQ2571691
Author name not available (Why is that?)
Publication date: 14 November 2005
Published in: (Search for Journal in Brave)
Abstract: We compute the limiting distributions of the largest eigenvalue of a complex Gaussian sample covariance matrix when both the number of samples and the number of variables in each sample become large. When all but finitely many, say , eigenvalues of the covariance matrix are the same, the dependence of the limiting distribution of the largest eigenvalue of the sample covariance matrix on those distinguished eigenvalues of the covariance matrix is completely characterized in terms of an infinite sequence of new distribution functions that generalize the Tracy-Widom distributions of the random matrix theory. Especially a phase transition phenomena is observed. Our results also apply to a last passage percolation model and a queuing model.
Full work available at URL: https://arxiv.org/abs/math/0403022
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