SPECTRAL PROPERTIES OF WIGNER MATRICES

2010/09/25 by Benjamin Schlein
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Computer science #Mathematical Analysis and Transform Methods #Mathematics #Physics #Pure mathematics #Quantum #Quantum mechanics #Random Matrices and Applications #Section (typography) #Spectral properties #Spectrum (functional analysis) #Statistical physics #Wigner distribution function #math-ph #math.MP

paper · pdf · doi:10.1142/9789814350365_0006

14 pages, contribution to the Proceedings of the Conference QMath 11 held in Hradec Kralove (Czechia) in September 2010

arxiv created 2010/09/25 · openalex publication_date 2011/05/01 · arxiv updated 2017/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In these notes we review recent progress (and, in Section \refsec:ados, we announce a new result) concerning the statistical properties of the spectrum of Wigner random matrices.

Citations

• Universality of the Local Spacing Distribution¶in Certain Ensembles of Hermitian Wigner Matrices
• Random matrices: Universality of local eigenvalue statistics
• Universality for generalized Wigner matrices with Bernoulli distribution
• Local Semicircle Law and Complete Delocalization for Wigner Random Matrices
• Random Matrices: Universality of Local Eigenvalue Statistics up to the Edge
• Rigidity of Eigenvalues of Generalized Wigner Matrices
• Universality of Random Matrices and Local Relaxation Flow
• The local relaxation flow approach to universality of the local statistics for random matrices
• Random matrices: Universality of local eigenvalue statistics
• Bulk universality for generalized Wigner matrices
• Characteristic Vectors of Bordered Matrices With Infinite Dimensions