RANDOM MATRICES: SHARP CONCENTRATION OF EIGENVALUES

DOI10.1142/S201032631350007XzbMath1296.15022arXiv1201.4789OpenAlexW2963473234MaRDI QIDQ2853397

Van H. Vu, Terence C. Tao

Publication date: 21 October 2013

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

Full work available at URL: https://arxiv.org/abs/1201.4789

zbMATH Keywords

eigenvaluesrandom matricesconcentration of measureWigner matricesLindenberg replacement argument

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)

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Cites Work

• A central limit theorem for the determinant of a Wigner matrix
• Random matrices: universality of local eigenvalue statistics
• Small deviations for beta ensembles
• Rigidity of eigenvalues of generalized Wigner matrices
• Local semicircle law and complete delocalization for Wigner random matrices
• Gaussian fluctuations of eigenvalues in Wigner random matrices
• Necessary and sufficient conditions for almost sure convergence of the largest eigenvalue of a Wigner matrix
• Gaussian fluctuations of eigenvalues in the GUE
• On the concentration of eigenvalues of random symmetric matrices
• Concentration of norms and eigenvalues of random matrices
• On orthogonal and symplectic matrix ensembles
• Random matrices: Universality of local eigenvalue statistics up to the edge
• Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices
• An Introduction to Random Matrices
• A Bound on Tail Probabilities for Quadratic Forms in Independent Random Variables
• Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices