Large complex correlated Wishart matrices: fluctuations and asymptotic independence at the edges
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Publication:726805
DOI10.1214/15-AOP1022zbMath1346.15035arXiv1409.7548MaRDI QIDQ726805
Jamal Najim, Walid Hachem, Adrien Hardy
Publication date: 14 July 2016
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1409.7548
eigenvalueBessel kernelasymptotic independencelarge random matricesWishart matrixTracy-Widom fluctuations
Random matrices (probabilistic aspects) (60B20) Strong limit theorems (60F15) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)
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Cites Work
- Unnamed Item
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- Large complex correlated Wishart matrices: the Pearcey kernel and expansion at the hard edge
- Gaussian fluctuations for linear spectral statistics of large random covariance matrices
- Limits of spiked random matrices. I
- Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices
- Almost sure localization of the eigenvalues in a Gaussian information plus noise model. Application to the spiked models.
- The outliers of a deformed Wigner matrix
- Gap probabilities for the generalized Bessel process: a Riemann-Hilbert approach
- Tracy-Widom distribution for the largest eigenvalue of real sample covariance matrices with general population
- The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
- A graph-based equilibrium problem for the limiting distribution of nonintersecting Brownian motions at low temperature
- Asymptotic independence in the spectrum of the Gaussian unitary ensemble
- Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
- Central limit theorems for eigenvalues in a spiked population model
- The largest eigenvalue of small rank perturbations of Hermitian random matrices
- Strong asymptotics for multiple Laguerre polynomials
- A universality result for the smallest eigenvalues of certain sample covariance matrices
- Random matrices: The distribution of the smallest singular values
- Universality results for the largest eigenvalues of some sample covariance matrix ensembles
- Spectral analysis of large dimensional random matrices
- A limit theorem for the norm of random matrices
- Limit laws for random matrices and free products
- No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices
- Level-spacing distributions and the Airy kernel
- Level spacing distributions and the Bessel kernel
- A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices
- Exact separation of eigenvalues of large dimensional sample covariance matrices
- On the distribution of the largest eigenvalue in principal components analysis
- CLT for linear spectral statistics of large-dimensional sample covariance matrices.
- Analysis of the limiting spectral distribution of large dimensional random matrices
- Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices
- The spectrum edge of random matrix ensembles.
- Shape fluctuations and random matrices
- Universality for the largest eigenvalue of sample covariance matrices with general population
- Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices
- The Tracy-Widom limit for the largest eigenvalues of singular complex Wishart matrices
- Universality of covariance matrices
- Eigenvalues of large sample covariance matrices of spiked population models
- Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
- Integral representations for multiple Hermite and multiple Laguerre polynomials.
- On the principal components of sample covariance matrices
- Random Matrix Methods for Wireless Communications
- PDEs SATISFIED BY EXTREME EIGENVALUES DISTRIBUTIONS OF GUE AND LUE
- RANDOM COVARIANCE MATRICES: UNIVERSALITY OF LOCAL STATISTICS OF EIGENVALUES UP TO THE EDGE
- Universality
- Rank 1 real Wishart spiked model
- A Phase Transition for Nonintersecting Brownian Motions, and the Painleve II Equation
- On the numerical evaluation of Fredholm determinants
- Eigenvalues and Condition Numbers of Random Matrices
- Asymptotic Statistics
- Increasing subsequences and the hard-to-soft edge transition in matrix ensembles
- Asymptotic independence of the extreme eigenvalues of Gaussian unitary ensemble
- Performance of Statistical Tests for Single-Source Detection Using Random Matrix Theory
- Universality of local eigenvalue statistics for some sample covariance matrices
- Numerical inverting of matrices of high order
- Numerical Inverting of Matrices of High Order. II
- Traces and determinants of linear operators
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