On minimal singular values of random matrices with correlated entries

DOI10.1142/S2010326315500069zbMath1348.15023arXiv1309.5711OpenAlexW2962748775MaRDI QIDQ3449978

Friedrich Götze, Alexey Naumov, Alexander Tikhomirov

Publication date: 30 October 2015

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

Full work available at URL: https://arxiv.org/abs/1309.5711

zbMATH Keywords

Stieltjes transformrandom matricessingular valuescircular lawelliptic lawnon-identically distributed entries

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Random matrices (probabilistic aspects) (60B20) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)

Related Items (11)

Coverings of random ellipsoids, and invertibility of matrices with i.i.d. heavy-tailed entries ⋮ Local elliptic law ⋮ Semicircle law for a matrix ensemble with dependent entries ⋮ Singular values distribution of squares of elliptic random matrices and type B Narayana polynomials ⋮ Limit theorems for two classes of random matrices with Gaussian entries ⋮ Concentration inequalities for random tensors ⋮ Brown measure and asymptotic freeness of elliptic and related matrices ⋮ Local laws for non-Hermitian random matrices and their products ⋮ Convergence and asymptotic approximations to universal distributions in probability ⋮ Spectrum of heavy-tailed elliptic random matrices ⋮ Polynomial Threshold Functions, Hyperplane Arrangements, and Random Tensors

Cites Work

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• Around the circular law
• Random matrices: universality of local eigenvalue statistics
• The circular law for random matrices
• Bilinear and quadratic variants on the Littlewood-Offord problem
• The Littlewood-Offord problem and invertibility of random matrices
• The Strong Elliptic Law. Twenty years later. Part I
• Asymptotic expansions for bivariate von Mises functionals

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