Strong convergence of ESD for large quaternion sample covariance matrices and correlation matrices when p/n → 0

DOI10.1142/S2010326320500057zbMath1444.60011OpenAlexW2944394107MaRDI QIDQ5107059

Xue Ding

Publication date: 22 April 2020

Published in: Random Matrices: Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s2010326320500057

zbMATH Keywords

strong convergencerandom matrixcorrelation matricesempirical spectral distribution (ESD)quaternion sample covariance matrices

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Random matrices (probabilistic aspects) (60B20) Strong limit theorems (60F15) Random matrices (algebraic aspects) (15B52)

Cites Work

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• Convergence of empirical spectral distributions of large dimensional quaternion sample covariance matrices
• On the semicircular law of large-dimensional random quaternion matrices
• Strong convergence of ESD for the generalized sample covariance matrices when \(p/n \rightarrow 0\)
• Geršgorin type theorems for quaternionic matrices
• Spectral analysis of large dimensional random matrices
• Convergence to the semicircle law
• Convergence of the largest eigenvalue of normalized sample covariance matrices when \(p\) and \(n\) both tend to infinity with their ratio converging to zero
• Limiting spectral distribution of normalized sample covariance matrices with \(p/n\to 0\)
• Convergence rates of the spectral distributions of large random quaternion self-dual Hermitian matrices
• Extreme eigenvalues of large dimensional quaternion sample covariance matrices
• Convergence rates of spectral distributions of large dimensional quaternion sample covariance matrices
• RANDOM RIGHT EIGENVALUES OF GAUSSIAN QUATERNIONIC MATRICES
• Eigenvalue distributions of beta-Wishart matrices
• Right eigenvalue equation in quaternionic quantum mechanics
• On the limit of the spectral distribution of large-dimensional random quaternion covariance matrices
• Quaternions and matrices of quaternions
• On the limit of extreme eigenvalues of large dimensional random quaternion matrices

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