Convergence rates of the spectral distributions of large random quaternion self-dual Hermitian matrices

DOI10.1007/s10955-014-1096-6zbMath1309.15055arXiv1312.3747OpenAlexW2073771214MaRDI QIDQ2254911

Yanqing Yin, Zhi-Dong Bai

Publication date: 6 February 2015

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.3747

zbMATH Keywords

GSEconvergence ratesrandom matrixspectral distributionsemicircular lawquaternion seld-dual Hermitian matrix

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Random matrices (probabilistic aspects) (60B20) Strong limit theorems (60F15) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52) Functional limit theorems; invariance principles (60F17)

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Cites Work

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• On the semicircular law of large-dimensional random quaternion matrices
• The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source. I
• The Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices
• Convergence rate of expected spectral distributions of large random matrices. I: Wigner matrices
• Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
• Characteristic vectors of bordered matrices with infinite dimensions
• On the distribution of the roots of certain symmetric matrices
• Spectral analysis of large dimensional random matrices
• The eigenvalues of random symmetric matrices
• Remarks on the convergence rate of the spectral distributions of Wigner matrices
• Level-spacing distributions and the Airy kernel
• A note on the convergence rate of the spectral distributions of large random matrices
• Rate of convergence to the semi-circular law
• Universality of local eigenvalue statistics in random matrices with external source
• Distributions of the Extreme Eigenvaluesof Beta–Jacobi Random Matrices
• Rate of Convergence to the Semicircular Law for the Gaussian Unitary Ensemble
• The Quaternion Calculus
• Quaternions and matrices of quaternions
• On the limit of extreme eigenvalues of large dimensional random quaternion matrices