Bounds for the Stieltjes transform and the density of states of Wigner matrices

DOI10.1007/s00440-014-0586-4zbMath1330.60014arXiv1311.0326OpenAlexW3104988763MaRDI QIDQ748436

Claudio Cacciapuoti, Benjamin Schlein, Anna V. Maltsev

Publication date: 29 October 2015

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.0326

zbMATH Keywords

rate of convergencerandom matricesWigner matricesrigidity of the eigenvalues

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Random linear operators (47B80) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (18)

Rank-uniform local law for Wigner matrices ⋮ Optimal bounds for convergence of expected spectral distributions to the semi-circular law ⋮ Local law and Tracy-Widom limit for sparse random matrices ⋮ Local semicircle law under weak moment conditions ⋮ Large deviation theorem for zeros of polynomials and Hermitian random matrices ⋮ Moment Inequalities for Linear and Nonlinear Statistics ⋮ On optimal bounds in the local semicircle law under four moment condition ⋮ Local Marchenko–Pastur law at the hard edge of the sample covariance ensemble ⋮ Local laws for non-Hermitian random matrices ⋮ Bulk universality for generalized Wigner matrices with few moments ⋮ Local Semicircle Law under Moment Conditions: The Stieltjes Transform, Rigidity, and Delocalization ⋮ Maximum of the characteristic polynomial of random unitary matrices ⋮ Gaussian fluctuations of the determinant of Wigner matrices ⋮ On the ubiquity of the Cauchy distribution in spectral problems ⋮ Local laws for non-Hermitian random matrices and their products ⋮ Convergence and asymptotic approximations to universal distributions in probability ⋮ Optimal multi-resolvent local laws for Wigner matrices ⋮ Local semicircle law under fourth moment condition

Cites Work

• Unnamed Item
• Delocalization and diffusion profile for random band matrices
• Spectral statistics of Erdős-Rényi graphs. I: Local semicircle law
• Averaging fluctuations in resolvents of random band matrices
• The local semicircle law for a general class of random matrices
• Local circular law for random matrices
• The local circular law. II: The edge case
• Random covariance matrices: universality of local statistics of eigenvalues
• The local circular law. III: General case
• Quantum diffusion and eigenfunction delocalization in a random band matrix model
• Random matrices: universality of local eigenvalue statistics
• Universality of random matrices and local relaxation flow
• Universality for generalized Wigner matrices with Bernoulli distribution
• Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation
• Quantum diffusion and delocalization for band matrices with general distribution
• Average density of states for Hermitian Wigner matrices
• Rigidity of eigenvalues of generalized Wigner matrices
• Spectral statistics of Erdős-Rényi graphs II: eigenvalue spacing and the extreme eigenvalues
• Local semicircle law and complete delocalization for Wigner random matrices
• Characteristic vectors of bordered matrices with infinite dimensions
• Rate of convergence to the semi-circular law
• Universality at the edge of the spectrum in Wigner random matrices.
• Gaussian fluctuations of eigenvalues in the GUE
• Bulk universality for generalized Wigner matrices
• Random matrices: Universality of local eigenvalue statistics up to the edge
• Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices
• Bulk universality for Wigner Hermite matrices with subexponential decay
• The local relaxation flow approach to universality of the local statistics for random matrices
• A necessary and sufficient condition for edge universality of Wigner matrices
• Universality of covariance matrices
• RANDOM COVARIANCE MATRICES: UNIVERSALITY OF LOCAL STATISTICS OF EIGENVALUES UP TO THE EDGE
• Universality of Wigner random matrices: a survey of recent results
• Bulk universality for Wigner matrices
• Wegner Estimate and Level Repulsion for Wigner Random Matrices
• Local Marchenko-Pastur law at the hard edge of sample covariance 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

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