2009/08/31 by Terence Tao, Van Vu · 8 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Cauchy distribution #Computer science #Eigenvalues and eigenvectors #Interlacing #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum mechanics #Random Matrices and Applications #Random matrix #Universality (dynamical systems) #math.PR #msc:15A52
paper · pdf · doi:10.1007/s00220-010-1044-5
24 pages, no figures, to appear, Comm. Math. Phys. One new reference added
arxiv created 2010/01/11 · openalex publication_date 2010/04/02 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This is a continuation of our earlier paper (Tao and Vu, http://arxiv.org/abs/0908.1982v4[math.PR] , 2010) on the universality of the eigenvalues of Wigner random matrices. The main new results of this paper are an extension of the results in Tao and Vu ( http://arxiv.org/abs/0908.1982v4[math.PR] , 2010) from the bulk of the spectrum up to the edge. In particular, we prove a variant of the universality results of Soshnikov (Commun Math Phys 207(3):697–733, 1999) for the largest eigenvalues, assuming moment conditions rather than symmetry conditions. The main new technical observation is that there is a significant bias in the Cauchy interlacing law near the edge of the spectrum which allows one to continue ensuring the delocalization of eigenvectors.