The singular values of the GOE

DOI10.1142/S2010326315500094zbMath1348.15022arXiv1502.05946OpenAlexW2962955602MaRDI QIDQ3449981

Michael La Croix, Folkmar A. Bornemann

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/1502.05946

zbMATH Keywords

random matricesdeterminantssingular valuesGaussian unitary ensembleLaguerre unitary ensemblegap probabilitiesGaussian orthogonal ensemble

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Exact distribution theory in statistics (62E15) Random matrices (probabilistic aspects) (60B20) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)

Related Items (8)

Singular values and evenness symmetry in random matrix theory ⋮ The singular values of the GUE (less is more) ⋮ Orthogonal and symplectic Harish-Chandra integrals and matrix product ensembles ⋮ Exponential growth of random determinants beyond invariance ⋮ An arithmetic property of moments of the \(\beta\)-Hermite ensemble and certain map enumerators ⋮ Interlacing Diffusions ⋮ The random matrix hard edge: rare events and a transition ⋮ Gaussian fluctuations of the determinant of Wigner matrices

Cites Work

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• A central limit theorem for the determinant of a Wigner matrix
• Fast approach to the tracy-widom law at the edge of GOE and GUE
• The behavior of eigenvalues and singular values under perturbations of restricted rank
• Interpretations of some parameter dependent generalizations of classical matrix ensembles
• On the Inversion of Certain Matrices
• Evenness symmetry and inter-relationships between gap probabilities in random matrix theory
• Determinants of Random Matrices and Jack Polynomials of Rectangular Shape
• Tridiagonal realization of the antisymmetric Gaussian β-ensemble

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