Local semicircle law under weak moment conditions

DOI10.1134/S1064562416030029zbMath1352.15039OpenAlexW2470103252MaRDI QIDQ334393

Friedrich Götze, Dmitry Timushev, Alexey Naumov, Alexander Tikhomirov

Publication date: 1 November 2016

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562416030029

zbMATH Keywords

eigenvalueseigenvectorsStieltjes transformssemicircle lawspectral distribution functionsymmetric random matrices

Mathematics Subject Classification ID

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

Cites Work

• Spectral statistics of Erdős-Rényi graphs. I: Local semicircle law
• The local semicircle law for a general class of random matrices
• Spectral statistics of Erdős-Rényi graphs II: eigenvalue spacing and the extreme eigenvalues
• Local semicircle law and complete delocalization for Wigner random matrices
• Bounds for the Stieltjes transform and the density of states of Wigner matrices
• On the distribution of the roots of certain symmetric matrices
• Gaussian fluctuations of eigenvalues in the GUE
• Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices
• A necessary and sufficient condition for edge universality of Wigner matrices
• Spectral theory of random matrices
• SPECTRA OF RANDOM SELF ADJOINT OPERATORS
• Limit Theorems for Two Classes of Random Matrices with Dependent Entries

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