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Large complex correlated wishart matrices: Fluctuations and asymptotic independence at the edges
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2016 (English)In: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 44, no 3, 2264-2348 p.Article in journal (Refereed) PublishedText
Abstract [en]

We study the asymptotic behavior of eigenvalues of large complex correlated Wishart matrices at the edges of the limiting spectrum. In this setting, the support of the limiting eigenvalue distribution may have several connected components. Under mild conditions for the population matrices, we show that for every generic positive edge of that support, there exists an extremal eigenvalue which converges almost surely toward that edge and fluctuates according to the Tracy-Widom law at the scale N-2/3. Moreover, given several generic positive edges, we establish that the associated extremal eigenvalue fluctuations are asymptotically independent. Finally, when the leftmost edge is the origin ( hard edge), the fluctuations of the smallest eigenvalue are described by mean of the Bessel kernel at the scale N-2.

Place, publisher, year, edition, pages
Institute of Mathematical Statistics, 2016. Vol. 44, no 3, 2264-2348 p.
Keyword [en]
Large random matrices, Wishart matrix, Tracy-Widom fluctuations, asymptotic independence, Bessel kernel
National Category
Discrete Mathematics
URN: urn:nbn:se:kth:diva-188446DOI: 10.1214/15-AOP1022ISI: 000376180700015ScopusID: 2-s2.0-84971222618OAI: diva2:937308
Knut and Alice Wallenberg Foundation, KAW 2010.0063

QC 20160615

Available from: 2016-06-15 Created: 2016-06-10 Last updated: 2016-06-15Bibliographically approved

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