Perturbations of diagonal matrices by band random matrices

2011/04/11 by Florent Benaych-Georges, Benaych-Georges, Florent, Nathanaël Enriquez +1
Mathematics · #15A52 #Advanced Algebra and Geometry #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Spectral Theory in Mathematical Physics #math.PR #msc:15A52

paper · pdf · doi:10.48550/arxiv.1104.1983

7 pages, 4 figures

openalex publication_date 2011/04/11 · arxiv created 2011/04/27 · arxiv updated 2011/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We exhibit an explicit formula for the spectral density of a (large) random matrix which is a diagonal matrix whose spectral density converges, perturbated by the addition of a symmetric matrix with Gaussian entries and a given (small) limiting variance profile.

Citations

• Limit laws for Random matrices and free products

Related

• Empirical spectral distribution of a matrix under perturbation
• The limit of the operator norm for random matrices with a variance profile
• Eigenvectors of a matrix under random perturbation
• On Asymptotic Expansions and Scales of Spectral Universality in Band Random Matrix Ensembles
• The largest eigenvalue of small rank perturbations of Hermitian random matrices