Bulk universality for deformed Wigner matrices

Abstract

We consider $N\times N$ 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 $N$.

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)

References in corpus (10)

• Local semicircle law and complete delocalization for Wigner random matrices
• Edge Universality of Beta Ensembles
• Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices
• Edge Universality for Deformed Wigner Matrices
• Bulk universality for deformed Wigner matrices
• Fluctuations of eigenvalues of matrix models and their applications
• Change of variables as a method to study general $\beta$-models: bulk universality
• Transport maps for Beta-matrix models and Universality
• On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble
• Extremal Eigenvalues and Eigenvectors of Deformed Wigner Matrices

Cited by in corpus (26)

• Random Matrices with Slow Correlation Decay
• Bulk universality for deformed Wigner matrices
• Edge Universality for non-Hermitian Random Matrices
• Stability of the Matrix Dyson Equation and Random Matrices with Correlations
• Eigenvectors distribution and quantum unique ergodicity for deformed Wigner matrices
• Spectrum of deformed random matrices and free probability
• Edge statistics of Dyson Brownian motion
• Large deviations for extreme eigenvalues of deformed Wigner random matrices
• Anisotropic local laws for random matrices
• Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case
• Local law and mesoscopic fluctuations of Dyson Brownian motion for general $\beta$ and potential
• Central limit theorem for mesoscopic eigenvalue statistics of deformed Wigner matrices and sample covariance matrices
• Fluctuations Of Linear Spectral Statistics Of Deformed Wigner Matrices
• Delocalization and continuous spectrum for ultrametric random operators
• Quenched universality for deformed Wigner matrices
• Universality of random matrices with correlated entries
• Local spectral statistics of the addition of random matrices
• The Spectral Norm of Random Inner-Product Kernel Matrices
• Universality of the least singular value for the sum of random matrices
• Isotropic self-consistent equations for mean-field random matrices
• Kronecker-product random matrices and a matrix least squares problem
• Universality of the least singular value for sparse random matrices
• Gaussian fluctuations for linear spectral statistics of deformed Wigner matrices
• Spiked sample covariance matrices with possibly multiple bulk components
• Mesoscopic Perturbations of Large Random Matrices
• Eigenvectors of the square grid plus GUE