Large complex correlated Wishart matrices: Fluctuations and asymptotic independence at the edges
نویسندگان
چکیده
منابع مشابه
Large Complex Correlated Wishart Matrices: Fluctuations and Asymptotic Independence at the Edges
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 co...
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The aim of this note is to provide a pedagogical survey of the recent works [30, 31] concerning the local behavior of the eigenvalues of large complex correlated Wishart matrices at the edges and cusp points of the spectrum: Under quite general conditions, the eigenvalues fluctuations at a soft edge of the limiting spectrum, at the hard edge when it is present, or at a cusp point, are respectiv...
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Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M dagger M where M is a complex matrix drawn from a normalized distribution P(M) approximately exp(-Tr [AMB M dagger]) with A and B positive definite (square) matrices of arbitrary dimensions. Such so-called correlated Wishart matrices occur in many fields ranging from information theo...
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Let W be a correlated complex non-central Wishart matrix defined through W = XX, where X is n × m (n ≥ m) complex Gaussian with non-zero mean Υ and non-trivial covariance Σ. We derive exact expressions for the cumulative distribution functions (c.d.f.s) of the extreme eigenvalues (i.e., maximum and minimum) of W for some particular cases. These results are quite simple, involving rapidly conver...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2016
ISSN: 0091-1798
DOI: 10.1214/15-aop1022