Invertibility of random matrices: Unitary and orthogonal perturbations

DOI10.1090/S0894-0347-2013-00771-7zbMath1290.60007arXiv1206.5180MaRDI QIDQ5401341

M. V. Rudel'son, R. V. Vershinin

Publication date: 13 March 2014

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.5180

zbMATH Keywords

random matricesinvertibilitysingle ring theorem

Mathematics Subject Classification ID

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

Related Items

Outliers in the single ring theorem, Local single ring theorem on optimal scale, Quantitative invertibility of non-Hermitian random matrices, Spectrum of random perturbations of Toeplitz matrices with finite symbols, Random matrices with prescribed eigenvalues and expectation values for random quantum states, On the singularity of adjacency matrices for random regular digraphs, Circular law for the sum of random permutation matrices, Invertibility of sparse non-Hermitian matrices, Smoothed analysis of symmetric random matrices with continuous distributions, Spectral gap of sparse bistochastic matrices with exchangeable rows, Sharp transition of the invertibility of the adjacency matrices of sparse random graphs, Outlier Eigenvalues for Deformed I.I.D. Random Matrices, Quantitative results for banded Toeplitz matrices subject to random and deterministic perturbations, Polynomial Threshold Functions, Hyperplane Arrangements, and Random Tensors

Cites Work

• Unnamed Item
• On the least singular value of random symmetric matrices
• Random matrices: universality of local eigenvalue statistics
• The single ring theorem
• Local semicircle law and complete delocalization for Wigner random matrices
• Random matrices: The distribution of the smallest singular values
• The circular law for random matrices
• Non-Gaussian non-Hermitian random matrix theory: phase transition and addition formalism
• Brown's spectral distribution measure for \(R\)-diagonal elements in finite von Neumann algebras
• Polynomial inequalities on measurable sets and their applications. II: Weighted measures
• Support convergence in the single ring theorem
• Random matrices: universality of ESDs and the circular law
• Bounds for Kac's master equation
• Invertibility of random matrices: norm of the inverse
• Inverse Littlewood-Offord theorems and the condition number of random discrete matrices
• The Littlewood-Offord problem and invertibility of random matrices
• Non-asymptotic theory of random matrices: extreme singular values
• Wegner Estimate and Level Repulsion for Wigner Random Matrices
• Invertibility of symmetric random matrices
• Polynomial inequalities on measurable sets and their applications