Local Semicircle Law under Moment Conditions: The Stieltjes Transform, Rigidity, and Delocalization

DOI10.1137/S0040585X97T988496zbMath1426.15056arXiv1510.07350OpenAlexW2804269102MaRDI QIDQ4641653

Friedrich Götze, Alexey Naumov, Alexander Tikhomirov

Publication date: 18 May 2018

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.07350

zbMATH Keywords

Stieltjes transformrandom matrixsymmetric matrixempirical distribution functionspeed of convergencelocal semicircle lawWigner lawdelocalization of eigenvectorsrigidity of eigenvalues

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Random matrices (algebraic aspects) (15B52)

Related Items (10)

Rank-uniform local law for Wigner matrices ⋮ Local law and Tracy-Widom limit for sparse random matrices ⋮ Moment Inequalities for Linear and Nonlinear Statistics ⋮ Rate of convergence for sparse sample covariance matrices ⋮ On optimal bounds in the local semicircle law under four moment condition ⋮ Bulk universality for generalized Wigner matrices with few moments ⋮ Local laws for non-Hermitian random matrices and their products ⋮ A sharp rate of convergence for the empirical spectral measure of a random unitary matrix ⋮ Convergence and asymptotic approximations to universal distributions in probability ⋮ Local semicircle law under fourth moment condition

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