2013/02/19 by Ji Oon Lee, Lee, Ji Oon, Kevin Schnelli +1
Mathematics · Physics and Astronomy · #15B52 #60B20 #82B44 #Advanced Algebra and Geometry #Delocalized electron #FOS: Mathematics #FOS: Physical sciences #Law #Mathematical Physics (math-ph) #Mathematics #Physics #Political science #Probability (math.PR) #Quantum mechanics #Random Matrices and Applications #Spectral Theory in Mathematical Physics #Statistical physics #math-ph #math.MP #math.PR #msc:15B52 #msc:60B20 #msc:82B44
paper · pdf · doi:10.48550/arxiv.1302.4532
60 pages
openalex publication_date 2013/02/19 · arxiv created 2013/09/15 · arxiv updated 2013/09/17 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
We consider Hermitian random matrices of the form H = W + \λ V, where\nW is a Wigner matrix and V a diagonal random matrix independent of W. We\nassume subexponential decay for the matrix entries of W and we choose\n\λ \∼ 1 so that the eigenvalues of W and \λ V are of the same\norder in the bulk of the spectrum. In this paper, we prove for a large class of\ndiagonal matrices V that the local deformed semicircle law holds for H,\nwhich is an analogous result to the local semicircle law for Wigner matrices.\nWe also prove complete delocalization of eigenvectors and other results about\nthe positions of eigenvalues.\n