Bulk universality for deformed Wigner matrices

2014/05/31 by Ji Oon Lee, Kevin Schnelli, Ben Stetler +2
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Circular law #Combinatorics #Diagonal #Diagonal matrix #Eigenvalues and eigenvectors #Geometry #Hermitian matrix #Mathematical physics #Mathematics #Matrix (chemical analysis) #Multivariate random variable #Physics #Pure mathematics #Quantum mechanics #Random Matrices and Applications #Random matrix #Random variable #Spectrum (functional analysis) #Statistics #Universality (dynamical systems) #math.PR

paper · pdf · doi:10.1214/15-aop1023

published as Annals of Probability 2016, Vol. 44, No. 3, 2349-2425 · Published at http://dx.doi.org/10.1214/15-AOP1023 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2016/05/01 · arxiv created 2016/06/07 · arxiv updated 2016/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider N× N random matrices of the form H=W+V where W is a real symmetric or complex Hermitian Wigner matrix and V is a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume subexponential decay for the matrix entries of W, and we choose V so that the eigenvalues of W and V are typically of the same order. For a large class of diagonal matrices V, we show that the local statistics in the bulk of the spectrum are universal in the limit of large N.

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